[ { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/nhb2h-bxd10", "eprint_id": 122349, "eprint_status": "archive", "datestamp": "2023-08-22 21:31:47", "lastmod": "2023-10-20 20:29:41", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Nesi-Vincenzo", "name": { "family": "Nesi", "given": "Vincenzo" } }, { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar" }, "orcid": "0000-0001-8369-3014" }, { "id": "Zaccagnino-Davide", "name": { "family": "Zaccagnino", "given": "Davide" }, "orcid": "0000-0001-6884-8452" }, { "id": "Mascia-Corrado", "name": { "family": "Mascia", "given": "Corrado" }, "orcid": "0000-0002-7294-492X" }, { "id": "Doglioni-Carlo", "name": { "family": "Doglioni", "given": "Carlo" }, "orcid": "0000-0002-8651-6387" } ] }, "title": "Tidal drag and westward drift of the lithosphere", "ispublished": "pub", "full_text_status": "public", "keywords": "General Earth and Planetary Sciences", "note": "\u00a9 2023 China University of Geosciences (Beijing) and Peking University Published by Elsevier. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). \n\nThe authors are grateful to a long list of colleagues who provided constructive criticism to the research. Vincenzo Nesi gratefully acknowledges support from Progetto di Ricerca 2020, Progetto di Ricerca di Ateneo 2021, \"Equazioni differenziali ellittiche e paraboliche non lineari\" Sapienza n. RM120172B8F74615; Oscar Bruno gratefully acknowledges support from NSF under contract DMS-2109831, from AFOSR under contract FA9550-21-1\u20130373, and from the NSSEFF Vannevar Bush Fellowship under ONR contract number N00014-16\u20131-2808; The research was also supported by ESA grant 4000133529/20/NL/GP (Doglioni). \n\nCRediT authorship contribution statement: Vincenzo Nesi: Conceptualization, Formal analysis, Investigation, Methodology, Software, Validation, Visualization, Writing - original draft, Writing - review & editing. Oscar Bruno: Conceptualization, Formal analysis, Investigation, Methodology, Validation. Davide Zaccagnino: Conceptualization, Investigation, Validation, Visualization, Writing - original draft, Writing - review & editing. Corrado Mascia: Conceptualization. Carlo Doglioni: Conceptualization, Funding acquisition, Project administration, Supervision, Visualization, Writing - review & editing. \n\nThe authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.\n\n
Published - 1-s2.0-S1674987123000907-main.pdf
", "abstract": "Tidal forces are generally neglected in the discussion about the mechanisms driving plate tectonics despite a worldwide geodynamic asymmetry also observed at subduction and rift zones. The tidal drag could theoretically explain the westerly shift of the lithosphere relative to the underlying mantle. Notwithstanding, viscosity in the asthenosphere is apparently too high to allow mechanical decoupling produced by tidal forces. Here, we propose a model for global scale geodynamics accompanied by numerical simulations of the tidal interaction of the Earth with the Moon and the Sun. We provide for the first time a theoretical proof that the tidal drag can produce a westerly motion of the lithosphere, also compatible with the slowing of the Earth's rotational spin. Our results suggest a westerly rotation of the lithosphere with a lower bound of w \u2248 (0.1 \u2013 0.2)\u00b0/Myr in the presence of a basal effective shear viscosity \u03b7 \u2248 10\u00b9\u2076 Pa\u2022s, but it may rise to w > 1\u00b0/Myr with a viscosity of \u03b7 \u227e 3 x 10\u00b9\u2074 Pa\u2022s within the Low-Velocity Zone (LVZ) atop the asthenosphere. This faster velocity would be more compatible with the mainstream of plate motion and the global asymmetry at plate boundaries. Based on these computations, we suggest that the super-adiabatic asthenosphere, being vigorously convecting, may further reduce the viscous coupling within the LVZ. Therefore, the combination of solid Earth tides, ultra-low viscosity LVZ and asthenospheric polarized small-scale convection may mechanically satisfy the large-scale decoupling of the lithosphere relative to the underlying mantle. Relative plate motions are explained because of lateral viscosity heterogeneities at the base of the lithosphere, which determine variable lithosphere-asthenosphere decoupling and plate interactions, hence plate tectonics.", "date": "2023-11", "date_type": "published", "publication": "Geoscience Frontiers", "volume": "14", "number": "6", "publisher": "Elsevier", "pagerange": "Art. No. 101623", "id_number": "CaltechAUTHORS:20230718-855965700.6", "issn": "1674-9871", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20230718-855965700.6", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Progetto di Ricerca", "grant_number": "RM120172B8F74615" }, { "agency": "NSF", "grant_number": "DMS-2109831" }, { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "FA9550-21-1-0373" }, { "agency": "National Security Science and Engineering Faculty Fellowship" }, { "agency": "Vannever Bush Faculty Fellowship" }, { "agency": "Office of Naval Research (ONR)", "grant_number": "N00014-16-1-2808" }, { "agency": "European Space Agency (ESA)", "grant_number": "4000133529/20/NL/GP" } ] }, "doi": "10.1016/j.gsf.2023.101623", "primary_object": { "basename": "1-s2.0-S1674987123000907-main.pdf", "url": "https://authors.library.caltech.edu/records/nhb2h-bxd10/files/1-s2.0-S1674987123000907-main.pdf" }, "resource_type": "article", "pub_year": "2023", "author_list": "Nesi, Vincenzo; Bruno, Oscar; et el." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/4mc28-0eh39", "eprint_id": 119233, "eprint_status": "archive", "datestamp": "2023-08-22 19:01:30", "lastmod": "2023-10-24 23:52:04", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bauinger-Christoph", "name": { "family": "Bauinger", "given": "Christoph" } }, { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar P." }, "orcid": "0000-0001-8369-3014" } ] }, "title": "Massively parallelized interpolated factored Green function method", "ispublished": "pub", "full_text_status": "public", "keywords": "Computer Science Applications; Physics and Astronomy (miscellaneous); Applied Mathematics; Computational Mathematics; Modeling and Simulation; Numerical Analysis", "note": "This work was supported by NSF, DARPA and AFOSR through contracts DMS-2109831 and HR00111720035, FA9550-19-1-0173 and FA9550-21-1-0373, and by the NSSEFF Vannevar Bush Fellowship under contract number N00014-16-1-2808.", "abstract": "This paper presents the first parallel implementation of the novel \"Interpolated Factored Green Function\" (IFGF) method introduced recently for the accelerated evaluation of discrete integral operators arising in wave scattering and other areas (Bauinger and Bruno, Jour. Computat. Phys., 2021). On the basis of the hierarchical IFGF interpolation strategy, the proposed (hybrid MPI-OpenMP) parallel implementation results in efficient data communication, and it scales up to large numbers of cores\u2014without any hard limitations on the number of cores efficiently employed. Moreover, on any given number of cores, the proposed parallel approach preserves the O(N log N) computing cost inherent in the sequential version of the IFGF algorithm. Unlike other approaches, the IFGF method does not utilize the Fast Fourier Transform (FFT), and it is thus better suited for efficient parallelization in distributed-memory computer systems. In particular, the IFGF method relies on a \"peer-to-peer\" strategy wherein, at every level, field propagation is directly enacted via \"exchanges\" between \"peer\" polynomials of constant degree, without data accumulation in large-scale \"telephone-central\" mathematical constructs such as those used in the Fast Multipole Method (FMM) and pure FFT-based approaches. A variety of numerical results presented in this paper illustrate the character of the proposed parallel algorithm, in particular demonstrating scaling from 1 to all 1,680 cores available in the High Performance Computing cluster used, and for problems of up to 4,096 wavelengths in acoustic size.", "date": "2023-02-15", "date_type": "published", "publication": "Journal of Computational Physics", "volume": "475", "publisher": "Elsevier", "pagerange": "Art. No. 111837", "id_number": "CaltechAUTHORS:20230213-460790900.1", "issn": "0021-9991", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20230213-460790900.1", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-2109831" }, { "agency": "Defense Advanced Research Projects Agency (DARPA)", "grant_number": "HR00111720035" }, { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "FA9550-19-1-0173" }, { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "FA9550-21-1-0373" }, { "agency": "National Security Science and Engineering Faculty Fellowship", "grant_number": "N00014-16-1-2808" } ] }, "doi": "10.1016/j.jcp.2022.111837", "resource_type": "article", "pub_year": "2023", "author_list": "Bauinger, Christoph and Bruno, Oscar P." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/kcaek-6wj52", "eprint_id": 118564, "eprint_status": "archive", "datestamp": "2023-08-20 08:49:08", "lastmod": "2023-10-24 23:24:21", "type": "monograph", "metadata_visibility": "show", "creators": { "items": [ { "id": "Maust-Haydn", "name": { "family": "Maust", "given": "Haydn" } }, { "id": "Li-Zongyi", "name": { "family": "Li", "given": "Zongyi" }, "orcid": "0000-0003-2081-9665" }, { "id": "Wang-Yixuan", "name": { "family": "Wang", "given": "Yixuan" }, "orcid": "0000-0001-7305-5422" }, { "id": "Leibovici-Daniel-V", "name": { "family": "Leibovici", "given": "Daniel" } }, { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar" }, "orcid": "0000-0001-8369-3014" }, { "id": "Hou-T-Y", "name": { "family": "Hou", "given": "Thomas" }, "orcid": "0000-0001-6287-1133" }, { "id": "Anandkumar-A", "name": { "family": "Anandkumar", "given": "Anima" }, "orcid": "0000-0002-6974-6797" } ] }, "title": "Fourier Continuation for Exact Derivative Computation in Physics-Informed Neural Operators", "ispublished": "unpub", "full_text_status": "public", "note": "H. Maust gratefully acknowledges the support of the Lynn A. Booth and Kent Kresa SURF Fellowship. Z. Li gratefully acknowledges the financial support from the Kortschak Scholars, PIMCO Fellows, and Amazon AI4Science Fellows programs. Oscar P. Bruno and Daniel Leibovici gratefully acknowledge support from NSF, AFOSR, and ONR through contracts DMS-2109831, FA9550-21-1-0373, and N00014-16-1-2808. T. Y. Hou is in part supported by the NSF grant DMS-2205590, the Choi Family Gift Fund, and the Charles Lee Powell endowed chair. A. Anandkumar is supported in part by Bren endowed chair.", "abstract": "The physics-informed neural operator (PINO) is a machine learning architecture that has shown promising empirical results for learning partial differential equations. PINO uses the Fourier neural operator (FNO) architecture to overcome the optimization challenges often faced by physics-informed neural networks. Since the convolution operator in PINO uses the Fourier series representation, its gradient can be computed exactly on the Fourier space. While Fourier series cannot represent nonperiodic functions, PINO and FNO still have the expressivity to learn nonperiodic problems with Fourier extension via padding. However, computing the Fourier extension in the physics-informed optimization requires solving an ill-conditioned system, resulting in inaccurate derivatives which prevent effective optimization. In this work, we present an architecture that leverages Fourier continuation (FC) to apply the exact gradient method to PINO for nonperiodic problems. This paper investigates three different ways that FC can be incorporated into PINO by testing their performance on a 1D blowup problem. Experiments show that FC-PINO outperforms padded PINO, improving equation loss by several orders of magnitude, and it can accurately capture the third order derivatives of nonsmooth solution functions.", "date": "2022-12-21", "date_type": "published", "publisher": "arXiv", "id_number": "CaltechAUTHORS:20221221-004750416", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20221221-004750416", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Caltech Summer Undergraduate Research Fellowship (SURF)" }, { "agency": "Kortschak Scholars Program" }, { "agency": "PIMCO" }, { "agency": "Amazon AI4Science Fellowship" }, { "agency": "NSF", "grant_number": "DMS-2109831" }, { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "FA9550-21-1-0373" }, { "agency": "National Security Science and Engineering Faculty Fellowship", "grant_number": "N00014-16-1-2808" }, { "agency": "NSF", "grant_number": "DMS-2205590" }, { "agency": "Choi Family Gift Fund" }, { "agency": "Charles Lee Powell Foundation" }, { "agency": "Bren Professor of Computing and Mathematical Sciences" } ] }, "doi": "10.48550/arXiv.2211.15960", "resource_type": "monograph", "pub_year": "2022", "author_list": "Maust, Haydn; Li, Zongyi; et el." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/t4hhq-j6046", "eprint_id": 115323, "eprint_status": "archive", "datestamp": "2023-08-22 18:00:57", "lastmod": "2023-10-24 16:26:16", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gaggioli-Enzo-L", "name": { "family": "Gaggioli", "given": "E. L." }, "orcid": "0000-0001-6939-6347" }, { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar P." }, "orcid": "0000-0001-8369-3014" } ] }, "title": "Parallel inverse-problem solver for time-domain optical tomography with perfect parallel scaling", "ispublished": "pub", "full_text_status": "public", "keywords": "Spectroscopy; Atomic and Molecular Physics, and Optics; Radiation", "note": "\u00a9 2022 Elsevier. \n\nReceived 17 February 2022, Revised 30 May 2022, Accepted 21 June 2022, Available online 24 June 2022, Version of Record 30 June 2022. \n\nThis work was supported by NSF, DARPA and AFOSR through contracts DMS-2109831 and HR00111720035 and FA9550-21-1-0373, and by the NSSEFF Vannevar Bush Fellowship under contract number N00014-16-1-2808. ELG acknowledge financial support from CONICET. \n\nThe codes utilized in this paper are available from the first author upon reasonable request. \n\nCRediT authorship contribution statement. E.L. Gaggioli: Conceptualization, Methodology, Software, Validation, Investigation, Visualization, Writing \u2013 original draft. Oscar P. Bruno: Conceptualization, Methodology, Validation, Investigation, Resources, Writing \u2013 original draft, Supervision, Funding acquisition. \n\nThe authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.\n\nSubmitted - 2202.09421.pdf
", "abstract": "This paper presents an efficient parallel radiative transfer-based inverse-problem solver for time-domain optical tomography. The radiative transfer equation provides a physically accurate model for the transport of photons in biological tissue, but the high computational cost associated with its solution has hindered its use in time-domain optical-tomography and other areas. In this paper this problem is tackled by means of a number of computational and modeling innovations, including (1) A spatial parallel-decomposition strategy with perfect parallel scaling for the forward and inverse problems of optical tomography on parallel computer systems; and, (2) A Multiple Staggered Source method (MSS) that solves the inverse transport problem at a computational cost that is independent of the number of sources employed, and which significantly accelerates the reconstruction of the optical parameters: a six-fold MSS acceleration factor is demonstrated in this paper. Finally, this contribution presents (3) An intuitive derivation of the adjoint-based formulation for evaluation of functional gradients, including the highly-relevant general Fresnel boundary conditions\u2014thus, in particular, generalizing results previously available for vacuum boundary conditions. Solutions of large and realistic 2D inverse problems are presented in this paper, which were produced on a 256-core computer system. The combined parallel/MSS acceleration approach reduced the required computing times by several orders of magnitude, from months to a few hours.", "date": "2022-11", "date_type": "published", "publication": "Journal of Quantitative Spectroscopy and Radiative Transfer", "volume": "290", "publisher": "Elsevier", "pagerange": "Art. No. 108300", "id_number": "CaltechAUTHORS:20220705-346498000", "issn": "0022-4073", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20220705-346498000", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-2109831" }, { "agency": "Defense Advanced Research Projects Agency (DARPA)", "grant_number": "HR00111720035" }, { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "FA9550-21-1-0373" }, { "agency": "Vannever Bush Faculty Fellowship" }, { "agency": "National Security Science and Engineering Faculty Fellowship", "grant_number": "N00014-16-1-2808" }, { "agency": "Consejo Nacional de Investigaciones Cient\u00edficas y T\u00e9cnicas (CONICET)" } ] }, "doi": "10.1016/j.jqsrt.2022.108300", "primary_object": { "basename": "2202.09421.pdf", "url": "https://authors.library.caltech.edu/records/t4hhq-j6046/files/2202.09421.pdf" }, "resource_type": "article", "pub_year": "2022", "author_list": "Gaggioli, E. L. and Bruno, Oscar P." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/9fpvg-18b09", "eprint_id": 115340, "eprint_status": "archive", "datestamp": "2023-08-22 16:04:00", "lastmod": "2023-10-24 16:27:09", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar P." }, "orcid": "0000-0001-8369-3014" }, { "id": "Hesthaven-Jan-S", "name": { "family": "Hesthaven", "given": "Jan S." }, "orcid": "0000-0001-8074-1586" }, { "id": "Leibovici-Daniel-V", "name": { "family": "Leibovici", "given": "Daniel V." } } ] }, "title": "FC-based shock-dynamics solver with neural-network localized artificial-viscosity assignment", "ispublished": "pub", "full_text_status": "public", "keywords": "Machine learning; Neural networks; Shock dynamics; Artificial viscosity; Fourier continuation; Non-periodic domain; Computer Science Applications; Physics and Astronomy (miscellaneous)", "note": "\u00a9 2022 The Authors. Published by Elsevier Under a Creative Commons license - Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0).\n\nReceived 29 October 2021, Revised 1 June 2022, Accepted 6 June 2022, Available online 9 June 2022, Version of Record 20 June 2022. \n\nOB and DL gratefully acknowledge support from NSF under contracts DMS-1714169 and DMS-2109831, from AFOSR under contract FA9550-21-1-0373, and from the NSSEFF Vannevar Bush Fellowship under ONR contract number N00014-16-1-2808. Initial conversations with J. Paul are also gratefully acknowledged. \n\nCRediT authorship contribution statement. Oscar P. Bruno: Conceptualization, Methodology, Validation, Investigation, Resources, Writing, Supervision, Funding acquisition. Jan Hesthaven: Conceptualization, Methodology, Investigation, Software, Resources. Daniel Leibovici: Conceptualization, Methodology, Software, Validation, Investigation, Writing, Visualization. \n\nThe authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.\n\nPublished - 1-s2.0-S2590055222000063-main.pdf
Submitted - 2111.01315.pdf
", "abstract": "This paper presents a spectral scheme for the numerical solution of nonlinear conservation laws in non-periodic domains under arbitrary boundary conditions. The approach relies on the use of the Fourier Continuation (FC) method for spectral representation of non-periodic functions in conjunction with smooth localized artificial viscosity assignments produced by means of a Shock-Detecting Neural Network (SDNN). Like previous shock capturing schemes and artificial viscosity techniques, the combined FC-SDNN strategy effectively controls spurious oscillations in the proximity of discontinuities. Thanks to its use of a localized but smooth artificial viscosity term, whose support is restricted to a vicinity of flow-discontinuity points, the algorithm enjoys spectral accuracy and low dissipation away from flow discontinuities, and, in such regions, it produces smooth numerical solutions\u2014as evidenced by an essential absence of spurious oscillations in level set lines. The FC-SDNN viscosity assignment, which does not require use of problem-dependent algorithmic parameters, induces a significantly lower overall dissipation than other methods, including the Fourier-spectral versions of the previous entropy viscosity method. The character of the proposed algorithm is illustrated with a variety of numerical results for the linear advection, Burgers and Euler equations in one and two-dimensional non-periodic spatial domains.", "date": "2022-06", "date_type": "published", "publication": "Journal of Computational Physics: X", "volume": "15", "publisher": "Elsevier", "pagerange": "Art. No. 100110", "id_number": "CaltechAUTHORS:20220705-346684000", "issn": "2590-0552", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20220705-346684000", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1714169" }, { "agency": "NSF", "grant_number": "DMS-2109831" }, { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "FA9550-21-1-0373" }, { "agency": "Vannever Bush Faculty Fellowship" }, { "agency": "National Security Science and Engineering Faculty Fellowship", "grant_number": "N00014-16-1-2808" } ] }, "doi": "10.1016/j.jcpx.2022.100110", "primary_object": { "basename": "1-s2.0-S2590055222000063-main.pdf", "url": "https://authors.library.caltech.edu/records/9fpvg-18b09/files/1-s2.0-S2590055222000063-main.pdf" }, "related_objects": [ { "basename": "2111.01315.pdf", "url": "https://authors.library.caltech.edu/records/9fpvg-18b09/files/2111.01315.pdf" } ], "resource_type": "article", "pub_year": "2022", "author_list": "Bruno, Oscar P.; Hesthaven, Jan S.; et el." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/avp1h-2zy53", "eprint_id": 113347, "eprint_status": "archive", "datestamp": "2023-08-22 15:48:55", "lastmod": "2023-10-23 23:03:04", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Fontana-Mauro", "name": { "family": "Fontana", "given": "Mauro" }, "orcid": "0000-0001-7636-9275" }, { "id": "Mininni-Pablo-D", "name": { "family": "Mininni", "given": "Pablo D." }, "orcid": "0000-0001-6858-6755" }, { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar P." }, "orcid": "0000-0001-8369-3014" }, { "id": "Dmitruk-Pablo", "name": { "family": "Dmitruk", "given": "Pablo" } } ] }, "title": "Vector potential-based MHD solver for non-periodic flows using Fourier continuation expansions", "ispublished": "pub", "full_text_status": "public", "keywords": "MHD; Non-periodic boundary conditions; Fourier continuation; Magnetic vector potential; Direct numerical simulations; General Physics and Astronomy; Hardware and Architecture", "note": "\u00a9 2022 Elsevier. \n\nReceived 15 July 2021, Revised 11 November 2021, Accepted 2 February 2022, Available online 8 February 2022. \n\nThe review of this paper was arranged by Prof. David W. Walker. \n\nThe authors acknowledge support from CONICET and ANPCyT through PIP, Argentina Grant No. 11220150100324CO, and PICT, Argentina Grant No. 2018-4298. This work was also supported by National Science Foundation, USA through contract DMS-1714169, and by the NSSEFF Vannevar Bush Fellowship, USA under contract number N0001416-1-2808. We also thank the Physics Department at the University of Buenos Aires for providing computing time on its Dirac cluster. \n\nThe authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.\n\nAccepted Version - 2107.07077.pdf
", "abstract": "A high-order method to evolve in time electromagnetic and velocity fields in conducting fluids with non-periodic boundaries is presented. The method has a small overhead compared with fast FFT-based pseudospectral methods in periodic domains. It uses the magnetic vector potential formulation for accurately enforcing the null divergence of the magnetic field, and allowing for different boundary conditions including perfectly conducting walls or vacuum surroundings, two cases relevant for many astrophysical, geophysical, and industrial flows. A spectral Fourier continuation method is used to accurately represent all fields and their spatial derivatives, allowing also for efficient solution of Poisson equations with different boundaries. A study of conducting flows at different Reynolds and Hartmann numbers, and with different boundary conditions, is presented to study convergence of the method and the accuracy of the solenoidal and boundary conditions.", "date": "2022-06", "date_type": "published", "publication": "Computer Physics Communications", "volume": "275", "publisher": "Elsevier", "pagerange": "Art. No. 108304", "id_number": "CaltechAUTHORS:20220209-266110000", "issn": "0010-4655", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20220209-266110000", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Consejo Nacional de Investigaciones Cient\u00edficas y T\u00e9cnicas (CONICET)", "grant_number": "11220150100324CO" }, { "agency": "Agencia Nacional de Promoci\u00f3n Cient\u00edfica y Tecnol\u00f3gica (ANPCyT)" }, { "agency": "Fondo para la Investigaci\u00f3n Cient\u00edfica y Tecnol\u00f3gica (FONCYT)", "grant_number": "2018-4298" }, { "agency": "NSF", "grant_number": "DMS-1714169" }, { "agency": "Vannever Bush Faculty Fellowship" }, { "agency": "National Security Science and Engineering Faculty Fellowship", "grant_number": "N0001416-1-2808" } ] }, "doi": "10.1016/j.cpc.2022.108304", "primary_object": { "basename": "2107.07077.pdf", "url": "https://authors.library.caltech.edu/records/avp1h-2zy53/files/2107.07077.pdf" }, "resource_type": "article", "pub_year": "2022", "author_list": "Fontana, Mauro; Mininni, Pablo D.; et el." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/62mx3-9ma39", "eprint_id": 116052, "eprint_status": "archive", "datestamp": "2023-08-22 15:13:11", "lastmod": "2023-10-23 19:45:19", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar P." }, "orcid": "0000-0001-8369-3014" }, { "id": "Paul-Jagabandhu", "name": { "family": "Paul", "given": "Jagabandhu" }, "orcid": "0000-0003-2375-0990" } ] }, "title": "Two-Dimensional Fourier Continuation and Applications", "ispublished": "pub", "full_text_status": "public", "keywords": "two-dimensional Fourier continuation; Poisson equation; wave equation; FC solver; Fourier forwarding; FFT; Applied Mathematics; Computational Mathematics", "note": "\u00a9 2022, Society for Industrial and Applied Mathematics. \n\nSubmitted to the journal's Methods and Algorithms for Scientific Computing section October 13, 2020; accepted for publication (in revised form) November 18, 2021; published electronically April 25, 2022. \n\nThis work was supported by the NSF through grants DMS-1714169, DMS-2109831, by DARPA through grant HR00111720035, by AFOSR through grant FA9550-21-1-0373, and by the Vannewar Bush Foundation through grant N00014-16-1-2808.\n\nPublished - 20m1373189.pdf
Submitted - 2010.03901.pdf
", "abstract": "This paper presents a \"two-dimensional Fourier Continuation\" method (2D-FC) for construction of bi-periodic extensions of smooth non-periodic functions defined over general two-dimensional smooth domains. The approach can be directly generalized to domains of any given dimensionality, and even to non-smooth domains, but such generalizations are not considered here. The 2D-FC extensions are produced in a two-step procedure. In the first step the one-dimensional Fourier Continuation method is applied along a discrete set of outward boundary-normal directions to produce, along such directions, continuations that vanish outside a narrow interval beyond the boundary. Thus, the first step of the algorithm produces \"blending-to-zero along normals\" for the given function values. In the second step, the extended function values are evaluated on an underlying Cartesian grid by means of an efficient, high-order boundary-normal interpolation scheme. A Fourier Continuation expansion of the given function can then be obtained by a direct application of the two-dimensional FFT algorithm. Algorithms of arbitrarily high order of accuracy can be obtained by this method. The usefulness and performance of the proposed two-dimensional Fourier Continuation method are illustrated with applications to the Poisson equation and the time-domain wave equation within a bounded domain. As part of these examples the novel \"Fourier Forwarding\" solver is introduced which, propagating plane waves as they would in free space and relying on certain boundary corrections, can solve the time-domain wave equation and other hyperbolic partial differential equations within general domains at computing costs that grow sublinearly with the size of the spatial discretization.", "date": "2022-04-25", "date_type": "published", "publication": "SIAM Journal on Scientific Computing", "volume": "44", "number": "2", "publisher": "SIAM", "pagerange": "A964-A992", "id_number": "CaltechAUTHORS:20220802-839163000", "issn": "1064-8275", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20220802-839163000", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1714169" }, { "agency": "NSF", "grant_number": "DMS-2109831" }, { "agency": "Defense Advanced Research Projects Agency (DARPA)", "grant_number": "HR00111720035" }, { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "FA9550-21-1-0373" }, { "agency": "Vannevar Bush Fellowship", "grant_number": "N00014-16-1-2808" } ] }, "doi": "10.1137/20m1373189", "primary_object": { "basename": "2010.03901.pdf", "url": "https://authors.library.caltech.edu/records/62mx3-9ma39/files/2010.03901.pdf" }, "related_objects": [ { "basename": "20m1373189.pdf", "url": "https://authors.library.caltech.edu/records/62mx3-9ma39/files/20m1373189.pdf" } ], "resource_type": "article", "pub_year": "2022", "author_list": "Bruno, Oscar P. and Paul, Jagabandhu" }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/7c5qy-6gj46", "eprint_id": 114069, "eprint_status": "archive", "datestamp": "2023-08-22 14:39:50", "lastmod": "2023-10-23 17:59:02", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Sideris-Constantine", "name": { "family": "Sideris", "given": "Constantine" }, "orcid": "0000-0002-3042-4889" }, { "id": "Khachaturian-Aroutin", "name": { "family": "Khachaturian", "given": "Aroutin" }, "orcid": "0000-0001-8304-3302" }, { "id": "White-Alexander-D", "name": { "family": "White", "given": "Alexander D." }, "orcid": "0000-0002-5387-310X" }, { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar P." }, "orcid": "0000-0001-8369-3014" }, { "id": "Hajimiri-A", "name": { "family": "Hajimiri", "given": "Ali" }, "orcid": "0000-0001-6736-8019" } ] }, "title": "Foundry-fabricated grating coupler demultiplexer inverse-designed via fast integral methods", "ispublished": "pub", "full_text_status": "public", "keywords": "Integrated optics; Nanophotonics and plasmonics; Silicon photonics", "note": "\u00a9 The Author(s) 2022. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/. \n\nReceived 05 May 2021; Accepted 21 February 2022; Published 23 March 2022. \n\nO.P.B. gratefully acknowledges support from NSF under contracts DMS-1714169 and DMS-2109831, from AFOSR under contract FA9550-21-1-0373, from DARPA under contract HR00111720035, and from the NSSEFF Vannevar Bush Fellowship under contract number N00014-16-1-2808. C.S. gratefully acknowledges support by the National Science Foundation under contracts CCF-1849965 and CCF-2047433, and AFOSR under contract FA9550-20-1-0087. The authors gratefully acknowledge financial support from Caltech RI2 Program under contract CIT-2021RI2-1. \n\nData availability: The design parameters that characterize the proposed device as well as an alternate device requiring smaller minimum feature sizes, are included in the Supplementary Notes 2 and 4. The data used to produce the figures can be obtained upon reasonable request from the corresponding author. \n\nCode availability: The computer codes used for simulation and design are available from the corresponding author upon reasonable request. \n\nContributions: C.S. and O.P.B. developed the inverse design framework used, and utilized it to obtain the proposed design. C.S., A.K., A.D.W., and S.A.H. developed the testing methodology including incorporating additional test structures for decoupling the losses of the device itself from those of the measurement setup. A.K., A.D.W., and C.S. characterized the fabricated design experimentally. C.S., A.K., and O.P.B. analyzed the measurement results and compared them against numerical simulations. All authors contributed to the preparation and review of the manuscript. \n\nThe authors declare no competing interests. \n\nPeer review information: Communications Physics thanks Ke Xu, Daniele Melati, and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.\n\nSideris, C., Khachaturian, A., White, A.D. et al. Author Correction: Foundry-fabricated grating coupler demultiplexer inverse-designed via fast integral methods. Commun Phys 5, 98 (2022). https://doi.org/10.1038/s42005-022-00877-4\n\nPublished - s42005-022-00839-w.pdf
Supplemental Material - 42005_2022_839_MOESM1_ESM.pdf
Supplemental Material - 42005_2022_839_MOESM2_ESM.pdf
Erratum - s42005-022-00877-4.pdf
", "abstract": "Silicon photonics is an emerging technology which, enabling nanoscale manipulation of light on chips, impacts areas as diverse as communications, computing, and sensing. Wavelength division multiplexing is commonly used to maximize throughput over a single optical channel by modulating multiple data streams on different wavelengths concurrently. Traditionally, wavelength (de)multiplexers are implemented as monolithic devices, separate from the grating coupler, used to couple light into the chip. This paper describes the design and measurement of a grating coupler demultiplexer\u2014a single device which combines both light coupling and demultiplexing capabilities. The device was designed by means of a custom inverse design algorithm which leverages boundary integral Maxwell solvers of extremely rapid convergence as the mesh is refined. To the best of our knowledge, the fabricated device enjoys the lowest insertion loss reported for grating demultiplexers, small size, high splitting ratio, and low coupling-efficiency imbalance between ports, while meeting the fabricability constraints of a standard UV lithography process.", "date": "2022-03-23", "date_type": "published", "publication": "Communications Physics", "volume": "5", "publisher": "Nature Publishing Group", "pagerange": "Art. No. 68", "id_number": "CaltechAUTHORS:20220324-224059015", "issn": "2399-3650", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20220324-224059015", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1714169" }, { "agency": "NSF", "grant_number": "DMS-2109831" }, { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "FA9550-21-1-0373" }, { "agency": "Defense Advanced Research Projects Agency (DARPA)", "grant_number": "HR00111720035" }, { "agency": "Vannevar Bush Fellowship" }, { "agency": "National Security Science and Engineering Faculty Fellowship", "grant_number": "N00014-16-1-2808" }, { "agency": "NSF", "grant_number": "CCF-1849965" }, { "agency": "NSF", "grant_number": "CCF-2047433" }, { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "FA9550-20-1-0087" }, { "agency": "Rothenberg Innovation Initiative (RI2)", "grant_number": "CIT-2021RI2-1" } ] }, "doi": "10.1038/s42005-022-00839-w", "primary_object": { "basename": "42005_2022_839_MOESM1_ESM.pdf", "url": "https://authors.library.caltech.edu/records/7c5qy-6gj46/files/42005_2022_839_MOESM1_ESM.pdf" }, "related_objects": [ { "basename": "42005_2022_839_MOESM2_ESM.pdf", "url": "https://authors.library.caltech.edu/records/7c5qy-6gj46/files/42005_2022_839_MOESM2_ESM.pdf" }, { "basename": "s42005-022-00839-w.pdf", "url": "https://authors.library.caltech.edu/records/7c5qy-6gj46/files/s42005-022-00839-w.pdf" }, { "basename": "s42005-022-00877-4.pdf", "url": "https://authors.library.caltech.edu/records/7c5qy-6gj46/files/s42005-022-00877-4.pdf" } ], "resource_type": "article", "pub_year": "2022", "author_list": "Sideris, Constantine; Khachaturian, Aroutin; et el." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/vmfw6-17z29", "eprint_id": 111055, "eprint_status": "archive", "datestamp": "2023-08-20 04:53:23", "lastmod": "2023-10-23 20:01:18", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gaggioli-Enzo", "name": { "family": "Gaggioli", "given": "E. L." }, "orcid": "0000-0001-6939-6347" }, { "id": "Mitnik-Dario-M", "name": { "family": "Mitnik", "given": "D. M." }, "orcid": "0000-0003-0193-0958" }, { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "O. P." }, "orcid": "0000-0001-8369-3014" } ] }, "title": "Skin effect in neutron transport theory", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2021 American Physical Society. \n\n(Received 25 February 2021; accepted 1 September 2021; published 20 September 2021) \n\nO.P.B. was supported by NSF through Contract No. DMS-1714169 and by the NSSEFF Vannevar Bush Fellowship under Contract No. N00014-16-1-2808. E.L.G. and D.M.M. gratefully acknowledge the financial support from the following Argentine institutions: Consejo Nacional de Investigaciones Cient\u00edficas y T\u00e9cnicas (CONICET), PIP 11220130100607, Agencia Nacional de Promoci\u00f3n Cient\u00edfica y Tecnol\u00f3gica (ANPCyT) PICT-2017-2945, and Universidad de Buenos Aires UBACyT 20020170100727BA.\n\nPublished - PhysRevE.104.L032801.pdf
", "abstract": "We identify a neutron-flux \"skin effect\" in the context of neutron transport theory. The skin effect, which emerges as a boundary layer at material interfaces, plays a critical role in a correct description of transport phenomena. A correct accounting of the boundary-layer structure helps bypass computational difficulties reported in the literature over the last several decades, and should lead to efficient numerical methods for neutron transport in two and three dimensions.", "date": "2021-09", "date_type": "published", "publication": "Physical Review E", "volume": "104", "number": "3", "publisher": "American Physical Society", "pagerange": "Art. No. L032801", "id_number": "CaltechAUTHORS:20210927-213255519", "issn": "2470-0045", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210927-213255519", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1714169" }, { "agency": "National Security Science and Engineering Faculty Fellowship", "grant_number": "N00014-16-1-2808" }, { "agency": "Consejo Nacional de Investigaciones Cient\u00edficas y T\u00e9cnicas (CONICET)", "grant_number": "PIP 11220130100607" }, { "agency": "Agencia Nacional de Promoci\u00f3n Cient\u00edfica y Tecnol\u00f3gica (ANPCyT)", "grant_number": "PICT-2017-2945" }, { "agency": "Universidad de Buenos Aires", "grant_number": "20020170100727BA" } ] }, "doi": "10.1103/physreve.104.L032801", "primary_object": { "basename": "PhysRevE.104.L032801.pdf", "url": "https://authors.library.caltech.edu/records/vmfw6-17z29/files/PhysRevE.104.L032801.pdf" }, "resource_type": "article", "pub_year": "2021", "author_list": "Gaggioli, E. L.; Mitnik, D. M.; et el." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/cmpg4-0zh09", "eprint_id": 98477, "eprint_status": "archive", "datestamp": "2023-08-22 10:11:32", "lastmod": "2023-10-18 17:24:02", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar P." }, "orcid": "0000-0001-8369-3014" }, { "id": "Xu-Liwei", "name": { "family": "Xu", "given": "Liwei" } }, { "id": "Yin-Tao", "name": { "family": "Yin", "given": "Tao" } } ] }, "title": "Weighted integral solvers for elastic scattering by open arcs in two dimensions", "ispublished": "pub", "full_text_status": "public", "keywords": "Calder\u00f3n relation; elasticity; open arc; second\u2010kind integral solver", "note": "\u00a9 2021 John Wiley & Sons, Ltd. \n\nIssue Online: 05 May 2021; Version of Record online: 25 February 2021; Accepted manuscript online: 25 January 2021; Manuscript accepted: 21 January 2021; Manuscript revised: 21 August 2020; Manuscript received: 21 February 2020. \n\nFunding information: Air Force Office of Scientific Research, FA9550\u201015\u20101\u20100043; Defense Advanced Research Projects Agency, HR00111720035; National Science Foundation, DMS\u20101714169; Office of Naval Research, N00014\u201016\u20101\u20102808. \n\n\nData Availability Statement: The authors confirm that the data supporting the findings of this study are available within the article.\n\nSubmitted - 1902.08687.pdf
", "abstract": "We present new methodologies for the numerical solution of problems of elastic scattering by open arcs in two dimensions. The algorithms utilize weighted versions of the classical elastic integral operators associated with Dirichlet and Neumann boundary conditions, where the integral weight accounts for (and regularizes) the singularity of the integral\u2010equation solutions at the open\u2010arc endpoints. Crucially, the method also incorporates a certain \"open\u2010arc elastic Calder\u00f3n relation\" introduced in this article, whose validity is demonstrated on the basis of numerical experiments, but whose rigorous mathematical proof is left for future work. (In fact, the aforementioned open\u2010arc elastic Calder\u00f3n relation generalizes a corresponding elastic Calder\u00f3n relation for closed surfaces, which is also introduced in this article, and for which a rigorous proof is included.) Using the open\u2010surface Calder\u00f3n relation in conjunction with spectrally accurate quadrature rules and the Krylov\u2010subspace linear algebra solver GMRES, the proposed overall open\u2010arc elastic solver produces results of high accuracy in small number of iterations, for both low and high frequencies. A variety of numerical examples in this article demonstrate the accuracy and efficiency of the proposed methodology.", "date": "2021-06-15", "date_type": "published", "publication": "International Journal for Numerical Methods in Engineering", "volume": "122", "number": "11", "publisher": "Wiley", "pagerange": "2733-2750", "id_number": "CaltechAUTHORS:20190906-093843706", "issn": "0029-5981", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190906-093843706", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "FA9550-15-1-0043" }, { "agency": "Defense Advanced Research Projects Agency (DARPA)", "grant_number": "HR00111720035" }, { "agency": "NSF", "grant_number": "DMS-1411876" }, { "agency": "Office of Naval Research (ONR)", "grant_number": "N00014\u201016\u20101\u20102808" } ] }, "doi": "10.1002/nme.6639", "primary_object": { "basename": "1902.08687.pdf", "url": "https://authors.library.caltech.edu/records/cmpg4-0zh09/files/1902.08687.pdf" }, "resource_type": "article", "pub_year": "2021", "author_list": "Bruno, Oscar P.; Xu, Liwei; et el." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/bp7b1-kp848", "eprint_id": 107370, "eprint_status": "archive", "datestamp": "2023-08-22 09:32:42", "lastmod": "2023-10-23 15:49:25", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bauinger-Christoph", "name": { "family": "Bauinger", "given": "Christoph" } }, { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar P." }, "orcid": "0000-0001-8369-3014" } ] }, "title": "\"Interpolated Factored Green Function\" method for accelerated solution of scattering problems", "ispublished": "pub", "full_text_status": "restricted", "keywords": "Scattering; Green function; Integral equations; Acceleration", "note": "\u00a9 2020 Elsevier Inc. \n\nAvailable online 4 January 2021. \n\nThis work was supported by NSF and DARPA under contracts DMS-1714169 and HR00111720035, and the NSSEFF Vannevar Bush Fellowship under ONR contract N00014-16-1-2808. \n\nCRediT authorship contribution statement: Oscar P. Bruno: Conceptualization, Methodology, Validation, Investigation, Resources, Writing, Supervision, Funding acquisition. Christoph Bauinger: Conceptualization, Methodology, Software, Validation, Investigation, Writing, Visualization. \n\nThe authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.", "abstract": "This paper presents a novel Interpolated Factored Green Function method (IFGF) for the accelerated evaluation of the integral operators in scattering theory and other areas. Like existing acceleration methods in these fields, the IFGF algorithm evaluates the action of Green function-based integral operators at a cost of O(N log N) operations for an N-point surface mesh. The IFGF strategy, which leads to an extremely simple algorithm, capitalizes on slow variations inherent in a certain Green function analytic factor, which is analytic up to and including infinity, and which therefore allows for accelerated evaluation of fields produced by groups of sources on the basis of a recursive application of classical interpolation methods. Unlike other approaches, the IFGF method does not utilize the Fast Fourier Transform (FFT), and is thus better suited than other methods for efficient parallelization in distributed-memory computer systems. Only a serial implementation of the algorithm is considered in this paper, however, whose efficiency in terms of memory and speed is illustrated by means of a variety of numerical experiments\u2014including a 43 min., single-core operator evaluation (on 10 GB of peak memory), with a relative error of 1.5\u00d710\u207b\u00b2, for a problem of acoustic size of 512 wavelengths.", "date": "2021-04-01", "date_type": "published", "publication": "Journal of Computational Physics", "volume": "430", "publisher": "Elsevier", "pagerange": "Art. No. 110095", "id_number": "CaltechAUTHORS:20210107-135537998", "issn": "0021-9991", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210107-135537998", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1714169" }, { "agency": "Defense Advanced Research Projects Agency (DARPA)", "grant_number": "HR00111720035" }, { "agency": "National Security Science and Engineering Faculty Fellowship", "grant_number": "N00014-16-1-2808" }, { "agency": "Vannever Bush Faculty Fellowship" } ] }, "doi": "10.1016/j.jcp.2020.110095", "resource_type": "article", "pub_year": "2021", "author_list": "Bauinger, Christoph and Bruno, Oscar P." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/7e4kz-by487", "eprint_id": 104110, "eprint_status": "archive", "datestamp": "2023-08-22 09:32:24", "lastmod": "2023-10-20 19:05:21", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar P." }, "orcid": "0000-0001-8369-3014" }, { "id": "Yin-Tao", "name": { "family": "Yin", "given": "Tao" } } ] }, "title": "A windowed Green function method for elastic scattering problems on a half-space", "ispublished": "pub", "full_text_status": "public", "keywords": "Elastic wave; Half-space; Windowed Green function; Boundary integral equation", "note": "\u00a9 2020 Elsevier B.V. \n\nReceived 29 May 2020, Revised 8 December 2020, Accepted 13 December 2020, Available online 15 January 2021. \n\nThis work was supported by NSF and AFOSR under contracts DMS-1714169 and FA9550-15-1-0043, and by the NSSEFF Vannevar Bush Fellowship under ONR contract N00014-16-1-2808. \n\nThe authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.\n\nSubmitted - 2006.00124.pdf
", "abstract": "This paper presents a windowed Green function (WGF) method for the numerical solution of problems of elastic scattering by \"locally-rough surfaces\" (i.e., local perturbations of a half space), under either Dirichlet or Neumann boundary conditions, and in both two and three spatial dimensions. The proposed WGF method relies on an integral-equation formulation based on the free-space Green function, together with smooth operator windowing (based on a \"slow-rise\" windowing function) and efficient high-order singular-integration methods. The approach avoids the evaluation of the expensive layer Green function for elastic problems on a half-space, and it yields uniformly fast convergence for all incident angles. Numerical experiments for both two and three dimensional problems are presented, demonstrating the accuracy and super-algebraically fast convergence of the proposed method as the window-size grows.", "date": "2021-04-01", "date_type": "published", "publication": "Computer Methods in Applied Mechanics and Engineering", "volume": "376", "publisher": "Elsevier", "pagerange": "Art. No. 113651", "id_number": "CaltechAUTHORS:20200629-081223570", "issn": "0045-7825", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20200629-081223570", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1714169" }, { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "FA9550-15-1-0043" }, { "agency": "Vannevar Bush Fellowship" }, { "agency": "National Security Science and Engineering Faculty Fellowship", "grant_number": "N00014-16-1-2808" } ] }, "doi": "10.1016/j.cma.2020.113651", "primary_object": { "basename": "2006.00124.pdf", "url": "https://authors.library.caltech.edu/records/7e4kz-by487/files/2006.00124.pdf" }, "resource_type": "article", "pub_year": "2021", "author_list": "Bruno, Oscar P. and Yin, Tao" }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/yr4mf-58906", "eprint_id": 90609, "eprint_status": "archive", "datestamp": "2023-09-22 22:50:47", "lastmod": "2023-10-23 23:29:59", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar P." }, "orcid": "0000-0001-8369-3014" }, { "id": "Garza-E", "name": { "family": "Garza", "given": "Emmanuel" }, "orcid": "0000-0003-1687-8216" } ] }, "title": "A Chebyshev-based rectangular-polar integral solver for scattering by geometries described by non-overlapping patches", "ispublished": "pub", "full_text_status": "public", "keywords": "Integral equations; Scattering problem; High-order accuracy; CAD representation; Rectangular-polar method; General geometries", "note": "\u00a9 2020 Elsevier Inc. \n\nReceived 12 July 2019, Revised 24 July 2020, Accepted 24 July 2020, Available online 5 August 2020. \n\nThe authors gratefully acknowledge support by NSF, AFOSR and DARPA through contracts DMS-1714169 and FA9550-15-1-0043 and HR00111720035, and the NSSEFF Vannevar Bush Fellowship under contract number N00014-16-1-2808. Additionally, the authors thank Dr. Edwin Jimenez and Dr. James Guzman for providing the processing of the CAD geometry used in Section 5.4. \n\nCRediT authorship contribution statement: Oscar P. Bruno: Conceptualization, Methodology, Validation, Investigation, Resources, Writing, Supervision, Funding acquisition. Emmanuel Garza: Conceptualization, Methodology, Software, Validation, Investigation, Writing, Visualization. \n\nThe authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.\n\nSubmitted - 1807.01813.pdf
", "abstract": "This paper introduces a high-order-accurate strategy for integration of singular kernels and edge-singular integral densities that appear in the context of boundary integral equation formulations for the problem of acoustic scattering. In particular, the proposed method is designed for use in conjunction with geometry descriptions given by a set of arbitrary non-overlapping logically-quadrilateral patches\u2014which makes the algorithm particularly well suited for computer-aided design (CAD) geometries. Fej\u00e9r's first quadrature rule is incorporated in the algorithm, to provide a spectrally accurate method for evaluation of contributions from far integration regions, while highly-accurate precomputations of singular and near-singular integrals over certain \"surface patches\" together with two-dimensional Chebyshev transforms and suitable surface-varying \"rectangular-polar\" changes of variables, are used to obtain the contributions for singular and near-singular interactions. The overall integration method is then used in conjunction with the linear-algebra solver GMRES to produce solutions for sound-soft open- and closed-surface scattering obstacles, including an application to an aircraft described by means of a CAD representation. The approach is robust, fast, and highly accurate: use of a few points per wavelength suffices for the algorithm to produce far-field accuracies of a fraction of a percent, and slight increases in the discretization densities give rise to significant accuracy improvements.", "date": "2020-11-15", "date_type": "published", "publication": "Journal of Computational Physics", "volume": "421", "publisher": "Elsevier", "pagerange": "Art. No. 109740", "id_number": "CaltechAUTHORS:20181102-090626983", "issn": "0021-9991", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20181102-090626983", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1714169" }, { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "FA9550-15-1-0043" }, { "agency": "Defense Advanced Research Projects Agency (DARPA)", "grant_number": "HR00111720035" }, { "agency": "National Security Science and Engineering Faculty Fellowship", "grant_number": "N00014-16-1-2808" }, { "agency": "Vannever Bush Faculty Fellowship" } ] }, "doi": "10.1016/j.jcp.2020.109740", "primary_object": { "basename": "1807.01813.pdf", "url": "https://authors.library.caltech.edu/records/yr4mf-58906/files/1807.01813.pdf" }, "resource_type": "article", "pub_year": "2020", "author_list": "Bruno, Oscar P. and Garza, Emmanuel" }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/4y3vp-ast90", "eprint_id": 104207, "eprint_status": "archive", "datestamp": "2023-08-22 07:04:05", "lastmod": "2023-10-20 19:10:40", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Fontana-M", "name": { "family": "Fontana", "given": "Mauro" }, "orcid": "0000-0001-7636-9275" }, { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar P." }, "orcid": "0000-0001-8369-3014" }, { "id": "Mininni-P-D", "name": { "family": "Mininni", "given": "Pablo D." }, "orcid": "0000-0001-6858-6755" }, { "id": "Dmitruk-P", "name": { "family": "Dmitruk", "given": "Pablo" } } ] }, "title": "Fourier continuation method for incompressible fluids with boundaries", "ispublished": "pub", "full_text_status": "public", "keywords": "Navier\u2013Stokes equation; Non-periodic boundary conditions; Spectral methods; Fourier continuation; Explicit time-stepping; Simulations", "note": "\u00a9 2020 Elsevier B.V. \n\nReceived 10 March 2020, Revised 17 June 2020, Accepted 29 June 2020, Available online 2 July 2020. \n\nThe review of this paper was arranged by David W. Walker. \n\nThe authors acknowledge support from PIP Grant No. 11220150100324CO and from PICT Grant No. 2015-3530. This work was also supported by NSF and AFOSR through contracts DMS-1714169 and FA9550-15-1-0043, and by the NSSEFF Vannevar Bush Fellowship under contract number N00014-16-1-2808. We also thank the Physics Department at the University of Buenos Aires for providing computing time on its Dirac\ncluster.\n\nSubmitted - 2002.01392.pdf
", "abstract": "We present a Fourier Continuation-based parallel pseudospectral method for incompressible fluids in cuboid non-periodic domains. The method produces dispersionless and dissipationless derivatives with fast spectral convergence inside the domain, and with very high order convergence at the boundaries. Incompressibility is imposed by solving a Poisson equation for the pressure. Being Fourier-based, the method allows for fast computation of spectral transforms. It is compatible with uniform grids (although refined or nested meshes can also be implemented), which in turn allows for explicit time integration at sufficiently high Reynolds numbers. Using a new parallel code named SPECTER we illustrate the method with two problems: channel flow, and plane Rayleigh-B\u00e9nard convection under the Boussinesq approximation. In both cases the method yields results compatible with previous studies using other high-order numerical methods, with mild requirements on the time step for stability.", "date": "2020-11", "date_type": "published", "publication": "Computer Physics Communications", "volume": "256", "publisher": "Elsevier", "pagerange": "Art. No. 107482", "id_number": "CaltechAUTHORS:20200702-121835661", "issn": "0010-4655", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20200702-121835661", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "PIP", "grant_number": "11220150100324CO" }, { "agency": "Proyectos de Investigaci\u00f3n Cient\u00edfica y Tecnol\u00f3gica (PICT)", "grant_number": "2015-3530" }, { "agency": "NSF", "grant_number": "DMS-1714169" }, { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "FA9550-15-1-0043" }, { "agency": "Vannevar Bush Fellowship" }, { "agency": "National Security Science and Engineering Faculty Fellowship", "grant_number": "N00014-16-1-2808" } ] }, "doi": "10.1016/j.cpc.2020.107482", "primary_object": { "basename": "2002.01392.pdf", "url": "https://authors.library.caltech.edu/records/4y3vp-ast90/files/2002.01392.pdf" }, "resource_type": "article", "pub_year": "2020", "author_list": "Fontana, Mauro; Bruno, Oscar P.; et el." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/1w18m-29a90", "eprint_id": 101662, "eprint_status": "archive", "datestamp": "2023-08-19 21:43:23", "lastmod": "2023-10-19 22:56:08", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar P." }, "orcid": "0000-0001-8369-3014" }, { "id": "Fernandez-Lado-A-G", "name": { "family": "Fernandez-Lado", "given": "Agustin G." } } ] }, "title": "On the evaluation of quasi-periodic Green functions and wave-scattering at and around Rayleigh-Wood anomalies", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 2020 Elsevier Inc. \n\nReceived 28 August 2019, Revised 6 February 2020, Accepted 17 February 2020, Available online 2 March 2020. \n\nThis work was supported by NSF and AFOSR through contracts DMS-1714169 and FA9550-15-1-0043, and by the NSSEFF Vannevar Bush Fellowship under contract number N00014-16-1-2808.\nDeclaration of Competing Interest:\nThe authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.", "abstract": "This article presents full-spectrum, well-conditioned, Green-function methodologies for evaluation of scattering by general periodic structures, which remains applicable on a set of challenging singular configurations, usually called Rayleigh-Wood (RW) anomalies (at which the quasi-periodic Green function ceases to exist), where most existing quasi-periodic solvers break down. After reviewing a variety of existing fast-converging numerical procedures commonly used to compute the classical quasi-periodic Green-function, the present work explores the difficulties they present around RW-anomalies and introduces the concept of hybrid \"spatial/spectral\" representations. Such expressions allow both the modification of existing methods to obtain convergence at RW-anomalies as well as the application of a slight generalization of the Woodbury-Sherman-Morrison formulae together with a limiting procedure to bypass the singularities. (Although, for definiteness, the overall approach is applied to the scalar (acoustic) wave-scattering problem in the frequency domain, the approach can be extended in a straightforward manner to the harmonic Maxwell's and elasticity equations.) Ultimately, this thorough study of RW-anomalies yields fast and highly-accurate solvers, which are demonstrated with a variety of simulations of wave-scattering phenomena by arrays of particles, crossed impenetrable and penetrable diffraction gratings and other related structures. In particular, the methods developed in this article can be used to \"upgrade\" classical approaches, resulting in algorithms that are applicable throughout the spectrum, and it provides new methods for cases where previous approaches are either costly or fail altogether. In particular, it is suggested that the proposed shifted Green function approach may provide the only viable alternative for treatment of three-dimensional high-frequency configurations with either one or two directions of periodicity. A variety of computational examples are presented which demonstrate the flexibility of the overall approach.", "date": "2020-06-01", "date_type": "published", "publication": "Journal of Computational Physics", "volume": "410", "publisher": "Elsevier", "pagerange": "Art. No. 109352", "id_number": "CaltechAUTHORS:20200302-143817282", "issn": "0021-9991", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20200302-143817282", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1714169" }, { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "FA9550-15-1-0043" }, { "agency": "National Security Science and Engineering Faculty Fellowship", "grant_number": "N00014-16-1-2808" }, { "agency": "Vannever Bush Faculty Fellowship" } ] }, "doi": "10.1016/j.jcp.2020.109352", "resource_type": "article", "pub_year": "2020", "author_list": "Bruno, Oscar P. and Fernandez-Lado, Agustin G." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/2thss-cb248", "eprint_id": 100317, "eprint_status": "archive", "datestamp": "2023-08-22 05:16:31", "lastmod": "2023-10-18 19:50:48", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar P." }, "orcid": "0000-0001-8369-3014" }, { "id": "Yin-Tao", "name": { "family": "Yin", "given": "Tao" } } ] }, "title": "Regularized integral equation methods for elastic scattering problems in three dimensions", "ispublished": "pub", "full_text_status": "public", "keywords": "Elastic waves; Combined field integral equations; Calder\u00f3n relation; Hyper-singular operator; High-order methods", "note": "\u00a9 2020 Elsevier Inc. \n\nReceived 28 September 2019, Revised 10 February 2020, Accepted 17 February 2020, Available online 3 March 2020. \n\nThis work was supported by NSF and AFOSR through contracts DMS-1714169 and FA9550-15-1-0043, respectively, and by the NSSEFF Vannevar Bush Fellowship under contract number N00014-16-1-2808.\n\nThe authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.\n\nSubmitted - 1909.12975.pdf
", "abstract": "This paper presents novel methodologies for the numerical simulation of scattering of elastic waves by both closed and open surfaces in three-dimensional space. The proposed approach utilizes new integral formulations as well as an extension to the elastic context of the efficient high-order singular-integration methods [13] introduced recently for the acoustic case. In order to obtain formulations leading to iterative solvers (GMRES) which converge in small numbers of iterations we investigate, theoretically and computationally, the character of the spectra of various operators associated with the elastic-wave Calder\u00f3n relation\u2014including some of their possible compositions and combinations. In particular, by relying on the fact that the eigenvalues of the composite operator NS are bounded away from zero and infinity, new uniquely-solvable, low-GMRES-iteration integral formulation for the closed-surface case are presented. The introduction of corresponding low-GMRES-iteration equations for the open-surface equations additionally requires, for both spectral quality as well as accuracy and efficiency, use of weighted versions of the classical integral operators to match the singularity of the unknown density at edges. Several numerical examples demonstrate the accuracy and efficiency of the proposed methodology.", "date": "2020-06-01", "date_type": "published", "publication": "Journal of Computational Physics", "volume": "410", "publisher": "Elsevier", "pagerange": "Art. No. 109350", "id_number": "CaltechAUTHORS:20191216-160134658", "issn": "0021-9991", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20191216-160134658", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1714169" }, { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "FA9550-15-1-0043" }, { "agency": "National Security Science and Engineering Faculty Fellowship", "grant_number": "N00014-16-1-2808" }, { "agency": "Vannever Bush Faculty Fellowship" } ] }, "doi": "10.1016/j.jcp.2020.109350", "primary_object": { "basename": "1909.12975.pdf", "url": "https://authors.library.caltech.edu/records/2thss-cb248/files/1909.12975.pdf" }, "resource_type": "article", "pub_year": "2020", "author_list": "Bruno, Oscar P. and Yin, Tao" }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/f8b4v-skd93", "eprint_id": 98474, "eprint_status": "archive", "datestamp": "2023-08-22 05:09:06", "lastmod": "2023-10-18 17:23:55", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar P." }, "orcid": "0000-0001-8369-3014" }, { "id": "Galkowski-J", "name": { "family": "Galkowski", "given": "Jeffrey" } } ] }, "title": "Domains without dense Steklov nodal sets", "ispublished": "pub", "full_text_status": "public", "keywords": "Steklov; High frequency; Nodal set", "note": "\u00a9 2020 The Author(s). This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. \n\nReceived 18 September 2019; Revised 23 April 2020; Published 11 June 2020. \n\nThanks to Agustin Fernandez Lado for writing the code numerical Steklov-eigenfunction solver and for providing the derivation presented in Appendix A. Thanks also to Jared Wunsch for suggesting part of the proof of Lemma 5.2 The authors are grateful to the American Institute of Mathematics where this research began. Thanks also to the anonymous referees for many helpful comments. J.G. is grateful to the National Science Foundation for support under the Mathematical Sciences Postdoctoral Research Fellowship DMS-1502661 and under DMS-1900434. O.B. gratefully acknowledges support by NSF, AFOSR and DARPA through contracts DMS-1714169, FA9550-15-1-0043 and HR00111720035, and the NSSEFF Vannevar Bush Fellowship under contract number N00014-16-1-2808.\n\nPublished - Bruno-Galkowski2020_Article_DomainsWithoutDenseSteklovNoda.pdf
Submitted - 1908.03307.pdf
", "abstract": "This article concerns the asymptotic geometric character of the nodal set of the eigenfunctions of the Steklov eigenvalue problem \u2212\u0394\u03d5_(\u03c3j) = 0, on \u03a9, \u2202_\u03bd\u03d5_(\u03c3j) = \u03c3_j\u03d5_(\u03c3j) on \u2202\u03a9 in two-dimensional domains \u03a9. In particular, this paper presents a dense family A of simply-connected two-dimensional domains with analytic boundaries such that, for each \u03a9\u2208A, the nodal set of the eigenfunction \u03d5_(\u03c3j) \"is not dense at scale \u03c3_j\u207b\u00b9\". This result addresses a question put forth under \"Open Problem 10\" in Girouard and Polterovich (J Spectr Theory 7(2):321\u2013359, 2017). In fact, the results in the present paper establish that, for domains \u03a9\u2208A, the nodal sets of the eigenfunctions \u03d5_(\u03c3j) associated with the eigenvalue \u03c3_j have starkly different character than anticipated: they are not dense at any shrinking scale. More precisely, for each \u03a9\u2208A there is a value r\u2081 > 0 such that for each j there is x_j \u2208 \u03a9 such that \u03d5_(\u03c3j) does not vanish on the ball of radius r\u2081 around x_j.", "date": "2020-06", "date_type": "published", "publication": "Journal of Fourier Analysis and Applications", "volume": "26", "number": "3", "publisher": "Springer", "pagerange": "Art. No. 45", "id_number": "CaltechAUTHORS:20190906-093833395", "issn": "1069-5869", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190906-093833395", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF Postdoctoral Fellowship", "grant_number": "DMS-1502661" }, { "agency": "NSF", "grant_number": "DMS-1900434" }, { "agency": "NSF", "grant_number": "DMS-1714169" }, { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "FA9550-15-1-0043" }, { "agency": "Defense Advanced Research Projects Agency (DARPA)", "grant_number": "HR00111720035" }, { "agency": "National Security Science and Engineering Faculty Fellowship", "grant_number": "N00014-16-1-2808" }, { "agency": "Vannever Bush Faculty Fellowship" } ] }, "doi": "10.1007/s00041-020-09753-7", "primary_object": { "basename": "1908.03307.pdf", "url": "https://authors.library.caltech.edu/records/f8b4v-skd93/files/1908.03307.pdf" }, "related_objects": [ { "basename": "Bruno-Galkowski2020_Article_DomainsWithoutDenseSteklovNoda.pdf", "url": "https://authors.library.caltech.edu/records/f8b4v-skd93/files/Bruno-Galkowski2020_Article_DomainsWithoutDenseSteklovNoda.pdf" } ], "resource_type": "article", "pub_year": "2020", "author_list": "Bruno, Oscar P. and Galkowski, Jeffrey" }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/b7w5p-63n02", "eprint_id": 90608, "eprint_status": "archive", "datestamp": "2023-08-19 21:04:29", "lastmod": "2023-10-19 14:37:48", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Anderson-T-G", "name": { "family": "Anderson", "given": "Thomas G." } }, { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar P." }, "orcid": "0000-0001-8369-3014" }, { "id": "Lyon-M", "name": { "family": "Lyon", "given": "Mark" } } ] }, "title": "High-order, Dispersionless \"Fast-Hybrid\" Wave Equation Solver. Part I: O(1) Sampling Cost via Incident-Field Windowing and Recentering", "ispublished": "pub", "full_text_status": "public", "keywords": "time-frequency hybrid solver, integral equations, transform methods, wave equation\nsolver, high-frequency quadrature, time-parallel method", "note": "\u00a9 2020 Society for Industrial and Applied Mathematics. \n\nSubmitted to the journal's Methods and Algorithms for Scientific Computing section March 25, 2019; accepted for publication (in revised form) January 27, 2020; published electronically April 27, 2020. \n\nThis work was supported by the AFOSR through grant FA9550-15-1-0043, by the NSF through grant DMS-1714169, by DARPA through grant HR00111720035, and by the NSSEFF Vannevar Bush Fellowship under contract number N00014-16-1-2808. The work of the first author was also supported by the DOE through grant DEFG02-97ER25308. \n\nThanks are due to Emmanuel Garza for facilitating the use of the existing 3D frequency-domain codes [20]. A number of valuable comments and suggestions by the reviewers are also thankfully acknowledged.\n\nPublished - 19m1251953.pdf
Submitted - 1807.02718.pdf
", "abstract": "This paper proposes a frequency/time hybrid integral-equation method for the time-dependent wave equation in two- and three-dimensional spatial domains. Relying on Fourier transformation in time, the method utilizes a fixed (time-independent) number of frequency-domain integral-equation solutions to evaluate, with superalgebraically small errors, time-domain solutions for arbitrarily long times. The approach relies on two main elements, namely: (1) a smooth time-windowing methodology that enables accurate band-limited representations for arbitrarily long time signals and (2) a novel Fourier transform approach which, in a time-parallel manner and without causing spurious periodicity effects, delivers numerically dispersionless spectrally accurate solutions. A similar hybrid technique can be obtained on the basis of Laplace transforms instead of Fourier transforms, but we do not consider the Laplace-based method in the present contribution. The algorithm can handle dispersive media, it can tackle complex physical structures, it enables parallelization in time in a straightforward manner, and it allows for time leaping---that is, solution sampling at any given time T at O(1)-bounded sampling cost, for arbitrarily large values of T, and without requirement of evaluation of the solution at intermediate times. The proposed frequency-time hybridization strategy, which generalizes to any linear partial differential equation in the time domain for which frequency-domain solutions can be obtained (including, e.g., the time-domain Maxwell equations) and which is applicable in a wide range of scientific and engineering contexts, provides significant advantages over other available alternatives, such as volumetric discretization, time-domain integral equations, and convolution quadrature approaches.", "date": "2020-04-27", "date_type": "published", "publication": "SIAM Journal on Scientific Computing", "volume": "42", "number": "2", "publisher": "Society for Industrial and Applied Mathematics", "pagerange": "A1348-A1379", "id_number": "CaltechAUTHORS:20181102-090208948", "issn": "1064-8275", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20181102-090208948", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "FA9550-15-1-0043" }, { "agency": "NSF", "grant_number": "DMS-1714169" }, { "agency": "Defense Advanced Research Projects Agency (DARPA)", "grant_number": "HR00111720035" }, { "agency": "National Security Science and Engineering Faculty Fellowship", "grant_number": "N00014-16-1-2808" }, { "agency": "Vannever Bush Faculty Fellowship" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG02-97ER25308" } ] }, "doi": "10.1137/19M1251953", "primary_object": { "basename": "1807.02718.pdf", "url": "https://authors.library.caltech.edu/records/b7w5p-63n02/files/1807.02718.pdf" }, "related_objects": [ { "basename": "19m1251953.pdf", "url": "https://authors.library.caltech.edu/records/b7w5p-63n02/files/19m1251953.pdf" } ], "resource_type": "article", "pub_year": "2020", "author_list": "Anderson, Thomas G.; Bruno, Oscar P.; et el." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/p5k2f-8mq66", "eprint_id": 104775, "eprint_status": "archive", "datestamp": "2023-08-19 19:52:46", "lastmod": "2023-10-20 20:50:11", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Ammari-H", "name": { "family": "Ammari", "given": "Habib" } }, { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar" }, "orcid": "0000-0001-8369-3014" }, { "id": "Imeri-K", "name": { "family": "Imeri", "given": "Kthim" } }, { "id": "Nigam-N", "name": { "family": "Nigam", "given": "Nilima" }, "orcid": "0000-0002-6739-1179" } ] }, "title": "Wave Enhancement Through Optimization of Boundary Conditions", "ispublished": "pub", "full_text_status": "public", "keywords": "Zaremba eigenvalue problem, boundary integral operators, mixed boundary\nconditions, metasurfaces", "note": "\u00a9 2020 by SIAM. \n\nSubmitted to the journal's Computational Methods in Science and Engineering section July 15, 2019; accepted for publication (in revised form) December 9, 2019; published electronically February 4, 2020.\n\nPublished - 19m1274651.pdf
Submitted - 1907.11170.pdf
", "abstract": "In this paper, we present a new and efficient approach for optimizing the transmission signal between two points in a cavity at a given frequency, by changing boundary conditions. The proposed approach makes use of recent results on the monotonicity of the eigenvalues of the mixed boundary value problem and on the sensitivity of Green's function to small changes in the boundary conditions. The switching of the boundary condition from Dirichlet to Neumann can be performed through the use of the recently modeled concept of metasurfaces which are comprised of coupled pairs of Helmholtz resonators. A variety of numerical experiments are presented to show the applicability and the accuracy of the proposed new methodology.", "date": "2020-02-04", "date_type": "published", "publication": "SIAM Journal on Scientific Computing", "volume": "42", "number": "1", "publisher": "Society for Industrial and Applied Mathematics", "pagerange": "B207-B224", "id_number": "CaltechAUTHORS:20200806-123557817", "issn": "1064-8275", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20200806-123557817", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "doi": "10.1137/19m1274651", "primary_object": { "basename": "1907.11170.pdf", "url": "https://authors.library.caltech.edu/records/p5k2f-8mq66/files/1907.11170.pdf" }, "related_objects": [ { "basename": "19m1274651.pdf", "url": "https://authors.library.caltech.edu/records/p5k2f-8mq66/files/19m1274651.pdf" } ], "resource_type": "article", "pub_year": "2020", "author_list": "Ammari, Habib; Bruno, Oscar; et el." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/cex31-r2052", "eprint_id": 99941, "eprint_status": "archive", "datestamp": "2023-08-19 19:11:15", "lastmod": "2023-10-18 18:56:09", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Sideris-C", "name": { "family": "Sideris", "given": "Constantine" }, "orcid": "0000-0002-3042-4889" }, { "id": "Garza-E", "name": { "family": "Garza", "given": "Emmanuel" }, "orcid": "0000-0003-1687-8216" }, { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar" }, "orcid": "0000-0001-8369-3014" } ] }, "title": "Ultrafast Simulation and Optimization of Nanophotonic Devices with Integral Equation Methods", "ispublished": "pub", "full_text_status": "public", "keywords": "inverse design, nanophotonic devices, fast Maxwell simulation/optimization, integral equations, high-order accuracy, computational electromagnetics", "note": "\u00a9 2019 American Chemical Society. \n\nReceived: August 7, 2019; Published: November 19, 2019. \n\nWe gratefully acknowledge support by AFOSR, NSF, and DARPA through, respectively, contracts FA9550-15-1-0043, DMS-1714169, and HR00111720035 as well as by the NSSEFF Vannevar Bush Fellowship under contract number N00014-16-1-2808. We also acknowledge support by the NSF under grant no. 1849965. \n\nThe authors declare no competing financial interest.\n\nSupplemental Material - ph9b01137_si_001.pdf
", "abstract": "Integrated photonics is poised to become a billion-dollar industry due to its vast array of applications. However, designing and modeling photonic devices remains challenging due to the lack of analytical solutions and difficulties with numerical simulation. Recently, inverse design has emerged as a promising approach for designing photonic devices; however, the current implementations require major computational effort due to their use of inefficient electromagnetic solvers based on finite-difference methods. Here we report a new, highly efficient method for simulating devices based on boundary integral equations that is orders of magnitude faster and more accurate than existing solvers, almost achieves spectral convergence, and is free from numerical dispersion. We develop an optimization framework using our solver based on the adjoint method to design new, ready-to-fabricate devices in just minutes on a single-core laptop. As a demonstration, we optimize three different devices: a nonadiabatic waveguide taper, a 1:2 1550 nm power splitter, and a vertical-incidence grating coupler.", "date": "2019-12-18", "date_type": "published", "publication": "ACS Photonics", "volume": "6", "number": "12", "publisher": "American Chemical Society", "pagerange": "3233-3240", "id_number": "CaltechAUTHORS:20191120-075203260", "issn": "2330-4022", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20191120-075203260", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "FA9550-15-1-0043" }, { "agency": "NSF", "grant_number": "DMS-1714169" }, { "agency": "Defense Advanced Research Projects Agency (DARPA)", "grant_number": "HR00111720035" }, { "agency": "National Security Science and Engineering Faculty Fellowship", "grant_number": "N00014-16-1-2808" }, { "agency": "NSF", "grant_number": "1849965" }, { "agency": "Vannever Bush Faculty Fellowship" } ] }, "doi": "10.1021/acsphotonics.9b01137", "primary_object": { "basename": "ph9b01137_si_001.pdf", "url": "https://authors.library.caltech.edu/records/cex31-r2052/files/ph9b01137_si_001.pdf" }, "resource_type": "article", "pub_year": "2019", "author_list": "Sideris, Constantine; Garza, Emmanuel; et el." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/kcb80-nff04", "eprint_id": 97494, "eprint_status": "archive", "datestamp": "2023-08-19 18:03:18", "lastmod": "2023-10-18 15:59:52", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gaggioli-E-L", "name": { "family": "Gaggioli", "given": "E. L." } }, { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "O. P." }, "orcid": "0000-0001-8369-3014" }, { "id": "Mitnik-D-M", "name": { "family": "Mitnik", "given": "D. M." } } ] }, "title": "Light transport with the equation of radiative transfer: the Fourier Continuation \u2013 Discrete Ordinates (FC\u2013DOM) Method", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2019 Published by Elsevier Ltd. \n\nReceived 14 March 2019, Revised 1 July 2019, Accepted 27 July 2019, Available online 28 July 2019.", "abstract": "We present a method for the treatment of the time dependent radiative transfer equation under the discrete ordinate approximation. The novelty of the proposed approach stems, in part, from the incorporation of a spectral method for the calculation of the spatial differential operators based on the Fourier Continuation procedure introduced recently by Bruno and co\u2013authors. This is a spatially dispersionless and high order method, which can handle arbitrary geometries, including those encountered in the forward model of light transport in optical tomography. We validate our theoretical results by comparison with analytic and experimental outcomes of the fluence measurements on tissue-like phantoms. The method makes it possible to calculate the time of flight of photons in random media efficiently and with high accuracy.", "date": "2019-10", "date_type": "published", "publication": "Journal of Quantitative Spectroscopy and Radiative Transfer", "volume": "236", "publisher": "Elsevier", "pagerange": "Art. No. 106589", "id_number": "CaltechAUTHORS:20190729-151529749", "issn": "0022-4073", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190729-151529749", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Consejo Nacional de Investigaciones Cient\u00edficas y T\u00e9cnicas (CONICET)" }, { "agency": "Universidad de Buenos Aires" }, { "agency": "NSF", "grant_number": "DMS-1714169" }, { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "FA9550-15-1-0043" }, { "agency": "NSF", "grant_number": "DMS-1411876" } ] }, "doi": "10.1016/j.jqsrt.2019.106589", "resource_type": "article", "pub_year": "2019", "author_list": "Gaggioli, E. L.; Bruno, O. P.; et el." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/jb52v-5r463", "eprint_id": 98475, "eprint_status": "archive", "datestamp": "2023-08-19 16:45:22", "lastmod": "2023-10-18 17:23:57", "type": "monograph", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar P." }, "orcid": "0000-0001-8369-3014" }, { "id": "Pandey-Ambuj", "name": { "family": "Pandey", "given": "Ambuj" }, "orcid": "0000-0003-3590-4459" } ] }, "title": "Fast, higher-order direct/iterative hybrid solver for scattering by Inhomogeneous media -- with application to high-frequency and discontinuous refractivity problems", "ispublished": "unpub", "full_text_status": "public", "note": "This work was supported by NSF and AFOSR through contracts DMS-1411876 and FA9550-15-1-0043, and by the NSSEFF Vannevar Bush Fellowship under contract number N00014-16-1-2808.\n\nSubmitted - 1907.05914.pdf
", "abstract": "This paper presents a fast high-order method for the solution of two-dimensional problems of scattering by penetrable inhomogeneous media, with application to high-frequency configurations containing (possibly) discontinuous refractivities. The method relies on a combination of a differential volumetric formulation and a boundary integral formulation. Thus, in the proposed approach the entire computational domain is partitioned into large numbers of volumetric spectral approximation patches which are then grouped into patch subsets for local direct solution; the interactions with the exterior domain are handled by means of a boundary integral equation. The resulting algorithm can be quite effective: after a modestly-demanding precomputation stage (whose results for a given frequency can be repeatedly used for arbitrarily chosen incidence angles), the proposed algorithm can accurately evaluate scattering by configurations including large and complex objects and/or high refractivity contrasts, including possibly refractive-index discontinuities, in fast single-core runs.", "date": "2019-09-06", "date_type": "published", "publisher": "arXiv", "id_number": "CaltechAUTHORS:20190906-093836815", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190906-093836815", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1411876" }, { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "FA9550-15-1-0043" }, { "agency": "National Security Science and Engineering Faculty Fellowship", "grant_number": "N00014-16-1-2808" }, { "agency": "Vannever Bush Faculty Fellowship" } ] }, "doi": "10.48550/arXiv.1907.05914", "primary_object": { "basename": "1907.05914.pdf", "url": "https://authors.library.caltech.edu/records/jb52v-5r463/files/1907.05914.pdf" }, "resource_type": "monograph", "pub_year": "2019", "author_list": "Bruno, Oscar P. and Pandey, Ambuj" }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/fytpa-btx57", "eprint_id": 98476, "eprint_status": "archive", "datestamp": "2023-08-19 15:50:50", "lastmod": "2023-10-18 17:24:00", "type": "monograph", "metadata_visibility": "show", "creators": { "items": [ { "id": "Amlani-F", "name": { "family": "Amlani", "given": "Faisal" } }, { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar P." }, "orcid": "0000-0001-8369-3014" }, { "id": "L\u00f3pez-V\u00e1zquez-J-C", "name": { "family": "L\u00f3pez-V\u00e1zquez", "given": "Jos\u00e9 Carlos" } }, { "id": "Trillo-C", "name": { "family": "Trillo", "given": "Cristina" } }, { "id": "Doval-A-F", "name": { "family": "Doval", "given": "\u00c1ngel F." } }, { "id": "Fern\u00e1ndez-J-L", "name": { "family": "Fern\u00e1ndez", "given": "Jos\u00e9 L." } }, { "id": "Rodr\u00edguez-G\u00f3mez-P", "name": { "family": "Rodr\u00edguez-G\u00f3mez", "given": "Pablo" } } ] }, "title": "Transient Propagation and Scattering of Quasi-Rayleigh Waves in Plates: Quantitative comparison between Pulsed TV-Holography Measurements and FC(Gram) elastodynamic simulations", "ispublished": "unpub", "full_text_status": "public", "keywords": "Ultrasonic nondestructive testing, Elastic waves in plates, Pulsed TV holography, Spectral simulation, Fourier continuation, High order accuracy", "note": "OB gratefully acknowledges support by NSF and AFOSR and DARPA\nthrough contracts DMS-1411876, DMS-1714169, FA9550-15-1-0043 and HR00111720035, and the NSSEFF Vannevar Bush Fellowship under contract number N00014-16-1-2808. The authors from the University of Vigo gratefully acknowledge support by the Spanish Ministerio de Econom\u00eda y Competitividad and the European Comission (ERDF) in the context of the Plan Nacional de I+D+i (project number DPI2011-26163), by the Subdirecci\u00f3n Xeral de Promoci\u00f3n Cient\u00edfica e Tecnol\u00f3xica universitaria da Xunta de Galicia in the context of the Plan Galego de I+D+i (project number 10PXIB303167PR) and supplementary co-funding from the Universidade de Vigo (contract number 09VIA07).\n\nSubmitted - 1905.05289.pdf
", "abstract": "We study the scattering of transient, high-frequency, narrow-band quasi-Rayleigh elastic waves by through-thickness holes in aluminum plates, in the framework of ultrasonic nondestructive testing (NDT) based on full-field optical detection. Sequences of the instantaneous two-dimensional (2-D) out-of-plane displacement scattering maps are measured with a self-developed PTVH system. The corresponding simulated sequences are obtained by means of an FC(Gram) elastodynamic solver introduced recently, which implements a full three-dimensional (3D) vector formulation of the direct linear-elasticity scattering problem. A detailed quantitative comparison between these experimental and numerical sequences, which is presented here for the first time, shows very good agreement both in the amplitude and the phase of the acoustic field in the forward, lateral and backscattering areas. It is thus suggested that the combination of the PTVH system and the FC(Gram) elastodynamic solver provides an effective ultrasonic inspection tool for plate-like structures, with a significant potential for ultrasonic NDT applications.", "date": "2019-09-06", "date_type": "published", "publisher": "arXiv", "id_number": "CaltechAUTHORS:20190906-093840280", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190906-093840280", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1411876" }, { "agency": "NSF", "grant_number": "DMS-1714169" }, { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "FA9550-15-1-0043" }, { "agency": "Defense Advanced Research Projects Agency (DARPA)", "grant_number": "HR00111720035" }, { "agency": "National Security Science and Engineering Faculty Fellowship", "grant_number": "N00014-16-1-2808" }, { "agency": "Vannever Bush Faculty Fellowship" }, { "agency": "Ministerio de Econom\u00eda y Competitividad (MINECO)" }, { "agency": "European Regional Development Fund", "grant_number": "DPI2011-26163" }, { "agency": "Subdirecci\u00f3n Xeral de Promoci\u00f3n Cient\u00edfica e Tecnol\u00f3xica universitaria da Xunta de Galicia", "grant_number": "10PXIB303167PR" }, { "agency": "Universidade de Vigo", "grant_number": "09VIA07" } ] }, "doi": "10.48550/arXiv.1905.05289", "primary_object": { "basename": "1905.05289.pdf", "url": "https://authors.library.caltech.edu/records/fytpa-btx57/files/1905.05289.pdf" }, "resource_type": "monograph", "pub_year": "2019", "author_list": "Amlani, Faisal; Bruno, Oscar P.; et el." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/s4t25-3nh13", "eprint_id": 93652, "eprint_status": "archive", "datestamp": "2023-08-22 02:16:53", "lastmod": "2023-10-20 17:19:16", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar P." }, "orcid": "0000-0001-8369-3014" }, { "id": "Cubillos-M", "name": { "family": "Cubillos", "given": "Max" } }, { "id": "Jimenez-E", "name": { "family": "Jimenez", "given": "Edwin" } } ] }, "title": "Higher-order implicit-explicit multi-domain compressible Navier-Stokes solvers", "ispublished": "pub", "full_text_status": "restricted", "keywords": "Navier-Stokes; Alternating direction implicit; Fourier continuation; Overset grid; High-order", "note": "\u00a9 2019 Elsevier. \n\nReceived 30 May 2018, Revised 16 February 2019, Accepted 19 February 2019, Available online 7 March 2019. \n\nThe authors gratefully acknowledge support by NSF and AFOSR and DARPA through contracts DMS-1411876, DMS-1714169, FA9550-15-1-0043 and HR00111720035, and the NSSEFF Vannevar Bush Fellowship under contract number N00014-16-1-2808.", "abstract": "This paper presents a new class of solvers for the subsonic compressible Navier-Stokes equations in general two- and three-dimensional multi-domains. Building up on the recent single-domain ADI-based high-order Navier-Stokes solvers (Bruno and Cubillos, Journal of Computational Physics 307 (2016) 476-495) this article presents multi-domain implicit-explicit methods of high-order of temporal accuracy. The proposed methodology incorporates: 1) A novel linear-cost implicit solver based on use of high-order backward differentiation formulae (BDF) and an alternating direction implicit approach (ADI); 2) A fast explicit solver; 3) Nearly dispersionless spectral spatial discretizations; and 4) A domain decomposition strategy that negotiates the interactions between the implicit and explicit domains. In particular, the implicit methodology is quasi-unconditionally stable (it does not suffer from CFL constraints for adequately resolved flows), and it can deliver orders of time accuracy between two and six in the presence of general boundary conditions. As demonstrated via a variety of numerical experiments in two and three dimensions, further, the proposed multi-domain parallel implicit-explicit implementations exhibit high-order convergence in space and time, robust stability properties, limited dispersion, and high parallel efficiency.", "date": "2019-08-15", "date_type": "published", "publication": "Journal of Computational Physics", "volume": "391", "publisher": "Elsevier", "pagerange": "322-346", "id_number": "CaltechAUTHORS:20190308-103045387", "issn": "0021-9991", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190308-103045387", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1411876" }, { "agency": "NSF", "grant_number": "DMS-1714169" }, { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "FA9550-15-1-0043" }, { "agency": "Defense Advanced Research Projects Agency (DARPA)", "grant_number": "HR00111720035" }, { "agency": "National Security Science and Engineering Faculty Fellowship" } ] }, "doi": "10.1016/j.jcp.2019.02.033", "resource_type": "article", "pub_year": "2019", "author_list": "Bruno, Oscar P.; Cubillos, Max; et el." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/2w86w-qy483", "eprint_id": 90584, "eprint_status": "archive", "datestamp": "2023-08-22 00:51:59", "lastmod": "2023-10-19 14:36:14", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar P." }, "orcid": "0000-0001-8369-3014" }, { "id": "Maas-M", "name": { "family": "Maas", "given": "Mart\u00edn" } } ] }, "title": "Shifted equivalent sources and FFT acceleration for periodic scattering problems, including Wood anomalies", "ispublished": "pub", "full_text_status": "public", "keywords": "Wood anomaly; Quasi-periodic Green function; Rough-surface scattering; Diffraction grating; Boundary integral equations; Ewald summation method", "note": "\u00a9 2018 Elsevier. \n\nReceived 23 May 2018, Revised 26 October 2018, Accepted 27 October 2018, Available online 1 November 2018. \n\nOB gratefully acknowledges support by NSF and AFOSR and DARPA through contracts DMS-1411876 and FA9550-15-1-0043 and HR00111720035, and the NSSEFF Vannevar Bush Fellowship under contract number N00014-16-1-2808. MM work was supported from a PhD fellowship of CONICET and the Bec.AR-Fullbright Argentine Presidential Fellowship in Science and Technology.\n\nAccepted Version - Shifted_equivalent_sources_and_FFT_acceleration_for_periodic_scattering_problems,_including_Wood_anomalies.pdf
Submitted - 1707.04950
", "abstract": "This paper introduces a fast algorithm, applicable throughout the electromagnetic spectrum, for the numerical solution of problems of scattering by periodic surfaces in two-dimensional space. The proposed algorithm remains highly accurate and efficient for challenging configurations including randomly rough surfaces, deep corrugations, large periods, near grazing incidences, and, importantly, Wood-anomaly resonant frequencies. The proposed approach is based on use of certain \"shifted equivalent sources\" which enable FFT acceleration of a Wood-anomaly-capable quasi-periodic Green function introduced recently (Bruno and Delourme (2014) [4]). The Green-function strategy additionally incorporates an exponentially convergent shifted version of the classical spectral series for the Green function. While the computing-cost asymptotics depend on the asymptotic configuration assumed, the computing costs rise at most linearly with the size of the problem for a number of important rough-surface cases we consider. In practice, single-core runs in computing times ranging from a fraction of a second to a few seconds suffice for the proposed algorithm to produce highly-accurate solutions in some of the most challenging contexts arising in applications.", "date": "2019-02-01", "date_type": "published", "publication": "Journal of Computational Physics", "volume": "378", "publisher": "Elsevier", "pagerange": "548-572", "id_number": "CaltechAUTHORS:20181101-141916128", "issn": "0021-9991", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20181101-141916128", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1411876" }, { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "FA9550-15-1-0043" }, { "agency": "Defense Advanced Research Projects Agency (DARPA)", "grant_number": "HR0011-17-2-0035" }, { "agency": "National Security Science and Engineering Faculty Fellowship", "grant_number": "N00014-16-1-2808" }, { "agency": "Consejo Nacional de Investigaciones Cient\u00edficas y T\u00e9cnicas (CONICET)" }, { "agency": "Comisi\u00f3n Fulbright Argentina" } ] }, "doi": "10.1016/j.jcp.2018.10.044", "primary_object": { "basename": "1707.04950", "url": "https://authors.library.caltech.edu/records/2w86w-qy483/files/1707.04950" }, "related_objects": [ { "basename": "Shifted_equivalent_sources_and_FFT_acceleration_for_periodic_scattering_problems,_including_Wood_anomalies.pdf", "url": "https://authors.library.caltech.edu/records/2w86w-qy483/files/Shifted_equivalent_sources_and_FFT_acceleration_for_periodic_scattering_problems,_including_Wood_anomalies.pdf" } ], "resource_type": "article", "pub_year": "2019", "author_list": "Bruno, Oscar P. and Maas, Mart\u00edn" }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/1c5zr-s2m65", "eprint_id": 86198, "eprint_status": "archive", "datestamp": "2023-08-19 07:02:39", "lastmod": "2023-10-18 19:21:16", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Acosta-G", "name": { "family": "Acosta", "given": "Gabriel" } }, { "id": "Borthagaray-J-P", "name": { "family": "Borthagaray", "given": "Juan Pablo" } }, { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar" }, "orcid": "0000-0001-8369-3014" }, { "id": "Maas-M", "name": { "family": "Maas", "given": "Mart\u00edn" } } ] }, "title": "Regularity theory and high order numerical methods for the (1D)-fractional Laplacian", "ispublished": "pub", "full_text_status": "public", "keywords": "Fractional Laplacian, hypersingular integral equations, high order numerical methods, Gegenbauer polynomials", "note": "\u00a9 2017 American Mathematical Society. \n\nReceived by the editor August 30, 2016, and, in revised form, March 16, 2017. Article electronically published on November 9, 2017. \n\nThis research was partially supported by CONICET under grant PIP 2014-2016 11220130100184CO. \n\nThe work of the first author was partially supported by CONICET, Argentina, under grant PIP 2014\u20132016 11220130100184CO. \n\nThe second and fourth author's and MM's efforts were made possible by a graduate fellowship from CONICET, Argentina.\n\nThe third author's efforts were supported by the US NSF and AFOSR through contracts DMS-1411876 and FA9550-15-1-0043, and by the NSSEFF Vannevar Bush Fellowship under contract number N00014-16-1-2808.\n\nSubmitted - 1608.08443.pdf
", "abstract": "This paper presents regularity results and associated high order numerical methods for one-dimensional fractional-Laplacian boundary-value problems. On the basis of a factorization of solutions as a product of a certain edge-singular weight \u03c9 times a \"regular\" unknown, a characterization of the regularity of solutions is obtained in terms of the smoothness of the corresponding right-hand sides. In particular, for right-hand sides which are analytic in a Bernstein ellipse, analyticity in the same Bernstein ellipse is obtained for the ``regular'' unknown. Moreover, a sharp Sobolev regularity result is presented which completely characterizes the co-domain of the fractional-Laplacian operator in terms of certain weighted Sobolev spaces introduced in (Babu\u0161ka and Guo, SIAM J. Numer. Anal. 2002). The present theoretical treatment relies on a full eigendecomposition for a certain weighted integral operator in terms of the Gegenbauer polynomial basis. The proposed Gegenbauer-based Nystr\u00f6m numerical method for the fractional-Laplacian Dirichlet problem, further, is significantly more accurate and efficient than other algorithms considered previously. The sharp error estimates presented in this paper indicate that the proposed algorithm is spectrally accurate, with convergence rates that only depend on the smoothness of the right-hand side. In particular, convergence is exponentially fast (resp. faster than any power of the mesh-size) for analytic (resp. infinitely smooth) right-hand sides. The properties of the algorithm are illustrated with a variety of numerical results.", "date": "2018", "date_type": "published", "publication": "Mathematics of Computation", "volume": "87", "number": "312", "publisher": "American Mathematical Society", "pagerange": "1821-1857", "id_number": "CaltechAUTHORS:20180502-133444210", "issn": "0025-5718", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180502-133444210", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Consejo Nacional de Investigaciones Cient\u00edficas y T\u00e9cnicas (CONICET)", "grant_number": "PIP 2014-2016 11220130100184CO" }, { "agency": "NSF", "grant_number": "DMS-1411876" }, { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "FA9550-15-1-0043" }, { "agency": "National Security Science and Engineering Faculty Fellowship", "grant_number": "N00014-16-1-2808" } ] }, "doi": "10.1090/mcom/3276", "primary_object": { "basename": "1608.08443.pdf", "url": "https://authors.library.caltech.edu/records/1c5zr-s2m65/files/1608.08443.pdf" }, "resource_type": "article", "pub_year": "2018", "author_list": "Acosta, Gabriel; Borthagaray, Juan Pablo; et el." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/tbpsh-6nf53", "eprint_id": 84038, "eprint_status": "archive", "datestamp": "2023-08-19 06:21:29", "lastmod": "2023-10-18 14:38:06", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Franco-M", "name": { "family": "Franco", "given": "M." }, "orcid": "0000-0002-3560-8599" }, { "id": "Barber-M", "name": { "family": "Barber", "given": "M." } }, { "id": "Maas-M", "name": { "family": "Maas", "given": "M." } }, { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "O." }, "orcid": "0000-0001-8369-3014" }, { "id": "Grings-F", "name": { "family": "Grings", "given": "F." } }, { "id": "Calzetta-E", "name": { "family": "Calzetta", "given": "E." } } ] }, "title": "Validity of the Kirchhoff approximation for the scattering of electromagnetic waves from dielectric, doubly periodic surfaces", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 2017 Optical Society of America. \n\nReceived 8 September 2017; revised 5 November 2017; accepted 6 November 2017; posted 6 November 2017 (Doc. ID 306582);\npublished 30 November 2017. \n\nFunding: Consejo Nacional de Investigaciones Cient\u00edficas y T\u00e9cnicas (CONICET); Universidad de Buenos Aires (UBA); Agencia Nacional de Promoci\u00f3n Cient\u00edfica y Tecnol\u00f3gica (ANPCyT) (PICT-2014-0647).", "abstract": "Accuracy of Kirchhoff approximation (KA) for rough-surface electromagnetic wave scattering is studied by comparison with accurate numerical solutions in the context of three-dimensional dielectric surfaces. The Kirchhoff tangent plane approximation is examined without resorting to the principle of stationary phase. In particular, it is shown that this additional assumption leads to zero cross-polarized backscattered power, but not the tangent plane approximation itself. Extensive numerical results in the case of a bisinusoidal surface are presented for a wide range of problem parameters: height-to-period, wavelength, incidence angles, and dielectric constants. In particular, this paper shows that the range of validity inherent in the KA includes surfaces whose curvature is not only much smaller, but also comparable to the incident wavelength, with errors smaller than 5% in total reflectivity, thus presenting a detailed and reliable source for the validity of the KA in a three-dimensional fully polarimetric formulation.", "date": "2017-12", "date_type": "published", "publication": "Journal of the Optical Society of America A", "volume": "34", "number": "12", "publisher": "Optical Society of America", "pagerange": "2266-2277", "id_number": "CaltechAUTHORS:20180102-154213561", "issn": "1084-7529", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180102-154213561", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Consejo Nacional de Investigaciones Cient\u00edficas y T\u00e9cnicas (CONICET)" }, { "agency": "Universidad de Buenos Aires" }, { "agency": "Agencia Nacional de Promoci\u00f3n Cient\u00edfica y Tecnol\u00f3gica (ANPCyT)", "grant_number": "PICT-2014-0647" } ] }, "doi": "10.1364/JOSAA.34.002266", "resource_type": "article", "pub_year": "2017", "author_list": "Franco, M.; Barber, M.; et el." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/wt28p-7t627", "eprint_id": 83932, "eprint_status": "archive", "datestamp": "2023-08-21 22:10:46", "lastmod": "2023-10-18 14:31:41", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Akhmetgaliyev-E", "name": { "family": "Akhmetgaliyev", "given": "Eldar" }, "orcid": "0000-0003-4031-2351" }, { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar P." }, "orcid": "0000-0001-8369-3014" } ] }, "title": "Regularized integral formulation of mixed Dirichlet-Neumann problems", "ispublished": "pub", "full_text_status": "public", "keywords": "Integral equations; Dirichlet-Neumann mixed boundary values; Zaremba problem; singularity structure; numerical method", "note": "\u00a9 2017 Rocky Mountain Mathematics Consortium. \n\nReceived by the editors on December 1, 2015, and in revised form on February 2, 2017. \n\nThe authors gratefully acknowledge support from AFOSR and NSF.\n\nPublished - euclid.jiea.1510282933.pdf
Submitted - 1508.03438.pdf
", "abstract": "This paper presents a theoretical discussion as well as novel solution algorithms for problems of scattering on smooth two-dimensional domains under Zaremba boundary conditions, for which Dirichlet and Neumann conditions are specified on various portions of the domain boundary. The theoretical basis of the proposed numerical methods, which is provided for the first time in the present contribution, concerns detailed information about the singularity structure of solutions of the Helmholtz operator under boundary conditions of Zaremba type. The new numerical method is based on the use of Green functions and integral equations, and it relies on the Fourier continuation method for regularization of all smooth-domain Zaremba singularities as well as newly derived quadrature rules which give rise to high-order convergence, even around Zaremba singular points. As demonstrated in this paper, the resulting algorithms enjoy high-order convergence, and they can be used to efficiently solve challenging Helmholtz boundary value problems and Laplace eigenvalue problems with high-order accuracy.", "date": "2017-11-10", "date_type": "published", "publication": "Journal of Integral Equations and Applications", "volume": "29", "number": "4", "publisher": "Rocky Mountain Mathematics Consortium", "pagerange": "493-529", "id_number": "CaltechAUTHORS:20171214-155422476", "issn": "0897-3962", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171214-155422476", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Air Force Office of Scientific Research (AFOSR)" }, { "agency": "NSF" } ] }, "doi": "10.1216/JIE-2017-29-4-493", "primary_object": { "basename": "1508.03438.pdf", "url": "https://authors.library.caltech.edu/records/wt28p-7t627/files/1508.03438.pdf" }, "related_objects": [ { "basename": "euclid.jiea.1510282933.pdf", "url": "https://authors.library.caltech.edu/records/wt28p-7t627/files/euclid.jiea.1510282933.pdf" } ], "resource_type": "article", "pub_year": "2017", "author_list": "Akhmetgaliyev, Eldar and Bruno, Oscar P." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/hhra6-jqp88", "eprint_id": 83930, "eprint_status": "archive", "datestamp": "2023-08-19 05:51:00", "lastmod": "2023-10-18 14:31:29", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar P." }, "orcid": "0000-0001-8369-3014" }, { "id": "Shipman-Stephen-P", "name": { "family": "Shipman", "given": "Stephen P." }, "orcid": "0000-0001-6620-6528" }, { "id": "Turc-Catalin", "name": { "family": "Turc", "given": "Catalin" } }, { "id": "Venakided-Stephanos", "name": { "family": "Venakides", "given": "Stephanos" } } ] }, "title": "Three-dimensional quasi-periodic shifted Green function throughout the spectrum, including Wood anomalies", "ispublished": "pub", "full_text_status": "public", "keywords": "scattering, periodic Green function, lattice sum,Wood anomaly, boundary-integral equations, electromagnetic computation", "note": "\u00a9 2017 The Author(s) Published by the Royal Society. \n\nReceived: 5 April 2017. Accepted: 28 September 2017. \n\nData accessibility: All data applicable to this paper are included in the article. \n\nAuthors' contributions: All authors are equally considered co-contributors in this article. \n\nThere are no competing interests relevant to this article. \n\nThis effort was supported by AFOSR, NSF and a NSSEFF Vannevar Bush Fellowship under contracts FA9550-15-1-0043, DMS-1411876 and N00014-16-1-2808 (O.P.B.); NSF DMS-0807325 (S.P.S.); NSF DMS-1312169 and DMS-1614270 (C.T.) and NSF DMS-1211638 (S.V.).\n\nSubmitted - 1704.01017.pdf
", "abstract": "This work, part II in a series, presents an efficient method for evaluation of wave scattering by doubly periodic diffraction gratings at or near what are commonly called 'Wood anomaly frequencies'. At these frequencies, there is a grazing Rayleigh wave, and the quasi-periodic Green function ceases to exist. We present a modification of the Green function by adding two types of terms to its lattice sum. The first type are transversely shifted Green functions with coefficients that annihilate the growth in the original lattice sum and yield algebraic convergence. The second type are quasi-periodic plane wave solutions of the Helmholtz equation which reinstate certain necessary grazing modes without leading to blow-up at Wood anomalies. Using the new quasi-periodic Green function, we establish, for the first time, that the Dirichlet problem of scattering by a smooth doubly periodic scattering surface at a Wood frequency is uniquely solvable. We also present an efficient high-order numerical method based on this new Green function for scattering by doubly periodic surfaces at and around Wood frequencies. We believe this is the first solver able to handle Wood frequencies for doubly periodic scattering problems in three dimensions. We demonstrate the method by applying it to acoustic scattering.", "date": "2017-11", "date_type": "published", "publication": "Proceedings of the Royal Society A: Mathematical, physical, and engineering sciences", "volume": "473", "number": "2207", "publisher": "Royal Society of London", "pagerange": "Art. No. 20170242", "id_number": "CaltechAUTHORS:20171214-152953856", "issn": "1364-5021", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171214-152953856", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "FA9550-15-1-0043" }, { "agency": "NSF", "grant_number": "DMS-1411876" }, { "agency": "National Security Science and Engineering Faculty Fellowship", "grant_number": "N00014-16-1-2808" }, { "agency": "NSF", "grant_number": "DMS-0807325" }, { "agency": "NSF", "grant_number": "DMS-1312169" }, { "agency": "NSF", "grant_number": "DMS-1614270" }, { "agency": "NSF", "grant_number": "DMS-1211638" } ] }, "doi": "10.1098/rspa.2017.0242", "pmcid": "PMC5719622", "primary_object": { "basename": "1704.01017.pdf", "url": "https://authors.library.caltech.edu/records/hhra6-jqp88/files/1704.01017.pdf" }, "resource_type": "article", "pub_year": "2017", "author_list": "Bruno, Oscar P.; Shipman, Stephen P.; et el." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/bzn7w-5cg95", "eprint_id": 79218, "eprint_status": "archive", "datestamp": "2023-08-19 04:51:45", "lastmod": "2023-10-26 14:42:38", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar P." }, "orcid": "0000-0001-8369-3014" }, { "id": "Garza-E", "name": { "family": "Garza", "given": "Emmanuel" }, "orcid": "0000-0003-1687-8216" }, { "id": "P\u00e9rez-Arancibia-C", "name": { "family": "P\u00e9rez-Arancibia", "given": "Carlos" }, "orcid": "0000-0003-1647-4019" } ] }, "title": "Windowed Green Function Method for Nonuniform Open-Waveguide Problems", "ispublished": "pub", "full_text_status": "public", "keywords": "Dielectric waveguides, electromagnetic scattering, green function, integral equations, open waveguides", "note": "\u00a9 2017 IEEE. \n\nManuscript received January 6, 2017; revised June 23, 2017; accepted June 28, 2017. Date of publication July 18, 2017; date of current version September 1, 2017. \n\nThe authors gratefully acknowledge support by NSF and AFOSR through contracts DMS-1411876 and FA9550-15-1-0043, and by the NSSEFF Vannevar Bush Fellowship under contract number N00014-16-1-2808.\n\nSubmitted - 1610.04939.pdf
", "abstract": "This contribution presents a novel Windowed Green Function (WGF) method for the solution of problems of wave propagation, scattering, and radiation for structures that include open (dielectric) waveguides, waveguide junctions, as well as launching and/or termination sites and other nonuniformities. Based on the use of a \"slow-rise\" smooth-windowing technique in conjunction with free-space Green functions and associated integral representations, the proposed approach produces numerical solutions with errors that decrease faster than any negative power of the window size. The proposed methodology bypasses some of the most significant challenges associated with waveguide simulation. In particular, the WGF approach handles spatially infinite dielectric waveguide structures without recourse to absorbing boundary conditions, it facilitates proper treatment of complex geometries, and it seamlessly incorporates the open-waveguide character and associated radiation conditions inherent in the problem under consideration. The overall WGF approach is demonstrated in this paper by means of a variety of numerical results for 2-D open-waveguide termination, launching and junction problems.", "date": "2017-09", "date_type": "published", "publication": "IEEE Transactions on Antennas and Propagation", "volume": "65", "number": "9", "publisher": "IEEE", "pagerange": "4684-4692", "id_number": "CaltechAUTHORS:20170719-171226860", "issn": "0018-926X", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170719-171226860", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1411876" }, { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "FA9550-15-1-0043" }, { "agency": "National Security Science and Engineering Faculty Fellowship", "grant_number": "N00014-16-1-2808" }, { "agency": "Vannever Bush Faculty Fellowship" } ] }, "doi": "10.1109/TAP.2017.2728118", "primary_object": { "basename": "1610.04939.pdf", "url": "https://authors.library.caltech.edu/records/bzn7w-5cg95/files/1610.04939.pdf" }, "resource_type": "article", "pub_year": "2017", "author_list": "Bruno, Oscar P.; Garza, Emmanuel; et el." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/05jay-4ta14", "eprint_id": 79120, "eprint_status": "archive", "datestamp": "2023-08-21 21:09:53", "lastmod": "2023-10-26 14:36:29", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "O. P." }, "orcid": "0000-0001-8369-3014" }, { "id": "P\u00e9rez-Arancibia-C", "name": { "family": "P\u00e9rez-Arancibia", "given": "C." }, "orcid": "0000-0003-1647-4019" } ] }, "title": "Windowed Green function method for the Helmholtz equation in the presence of multiply layered media", "ispublished": "pub", "full_text_status": "public", "keywords": "Sommerfeld integral; layered media; integral equation; scattering", "note": "\u00a9 2017 The Author(s). Published by the Royal Society. \n\nReceived: 2 March 2017; Accepted: 11 May 2017; Published 14 June 2017. \n\nThis work was supported by NSF and AFOSR through contracts DMS-1411876 and FA9550-15-1-0043, and by the NSSEFF Vannevar Bush Fellowship under contract number N00014-16-1-2808. \n\nAuthors' contributions: O.P.B. and C.P.-A. contributed to all aspects of this article. \n\nWe declare we have no competing interests.\n\nSubmitted - 1703.01034.pdf
", "abstract": "This paper presents a new methodology for the solution of problems of two- and three-dimensional acoustic scattering (and, in particular, two-dimensional electromagnetic scattering) by obstacles and defects in the presence of an arbitrary number of penetrable layers. Relying on the use of certain slow-rise windowing functions, the proposed windowed Green function approach efficiently evaluates oscillatory integrals over unbounded domains, with high accuracy, without recourse to the highly expensive Sommerfeld integrals that have typically been used to account for the effect of underlying planar multilayer structures. The proposed methodology, whose theoretical basis was presented in the recent contribution (Bruno et al. 2016 SIAM J. Appl. Math. 76, 1871\u20131898. (doi:10.1137/15M1033782)), is fast, accurate, flexible and easy to implement. Our numerical experiments demonstrate that the numerical errors resulting from the proposed approach decrease faster than any negative power of the window size. In a number of examples considered in this paper, the proposed method is up to thousands of times faster, for a given accuracy, than corresponding methods based on the use of Sommerfeld integrals.", "date": "2017-06", "date_type": "published", "publication": "Proceedings of the Royal Society A: Mathematical, physical, and engineering sciences", "volume": "473", "number": "2202", "publisher": "Royal Society of London", "pagerange": "Art. No. 20170161", "id_number": "CaltechAUTHORS:20170717-085623869", "issn": "1364-5021", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170717-085623869", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1411876" }, { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "FA9550-15-1-0043" }, { "agency": "National Security Science and Engineering Faculty Fellowship", "grant_number": "N00014-16-1-2808" }, { "agency": "Vannever Bush Faculty Fellowship" } ] }, "doi": "10.1098/rspa.2017.0161", "pmcid": "PMC5493953", "primary_object": { "basename": "1703.01034.pdf", "url": "https://authors.library.caltech.edu/records/05jay-4ta14/files/1703.01034.pdf" }, "resource_type": "article", "pub_year": "2017", "author_list": "Bruno, O. P. and P\u00e9rez-Arancibia, C." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/exker-2rz06", "eprint_id": 77946, "eprint_status": "archive", "datestamp": "2023-08-19 02:38:52", "lastmod": "2023-10-25 23:35:23", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar P." }, "orcid": "0000-0001-8369-3014" }, { "id": "Cubillos-M", "name": { "family": "Cubillos", "given": "Max" } } ] }, "title": "On the Quasi-unconditional Stability of BDF-ADI Solvers for the Compressible Navier-Stokes Equations and Related Linear Problems", "ispublished": "pub", "full_text_status": "public", "keywords": "Navier-Stokes, quasi-unconditional stability, high-order, ADI, BDF, unconditional stability", "note": "\u00a9 2017 Society for Industrial and Applied Mathematics.\n\nReceived by the editors October 2, 2015; accepted for publication (in revised form) December 21, 2016; published electronically April 18, 2017. \n\nThe work of the first author was supported by AFOSR, NSF and an NSSEFF Vannevar Bush Fellowship under contracts FA9550-15-1-0043, DMS-1411876 and N00014-16-1-2808.\n\nPublished - 15m1042279.pdf
Submitted - 1509.09213.pdf
", "abstract": "The companion paper \"Higher-order in time quasi-unconditionally stable ADI solvers for the compressible Navier-Stokes equations in 2D and 3D curvilinear domains,\" which is referred to as Part I in what follows, introduces ADI (alternating direction implicit) solvers of higher orders of temporal accuracy (orders s = 2 to 6) for the compressible Navier-Stokes equations in two- and three-dimensional space. The proposed methodology employs the backward differentiation formulae (BDF) together with a quasilinear-like formulation, high-order extrapolation for nonlinear components, and the Douglas-Gunn splitting. A variety of numerical results presented in Part I demonstrate in practice the theoretical convergence rates enjoyed by these algorithms, as well as their excellent accuracy and stability properties for a wide range of Reynolds numbers. In particular, the proposed schemes enjoy a certain property of \"quasi-unconditional stability\": for small enough (problem-dependent) fixed values of the timestep \u0394t, these algorithms are stable for arbitrarily fine spatial discretizations. The present contribution presents a mathematical basis for the observed performance of these algorithms. Short of providing stability theorems for the full Navier-Stokes BDF-ADI solvers, this paper puts forth a number of stability proofs for BDF-ADI schemes as well as some related unsplit BDF schemes for a variety of related linear model problems in one, two, and three spatial dimensions. These include proofs of quasi-unconditional stability for unsplit BDF schemes of orders 2 \u2264 s \u2264 6, and even a proof of a form of unconditional stability for two-dimensional BDF-ADI schemes of order 2 for both convection and diffusion problems. Additionally, a set of numerical tests presented in this paper for the compressible Navier-Stokes equation indicate that quasi-unconditional stability carries over to the fully nonlinear context.", "date": "2017-04-18", "date_type": "published", "publication": "SIAM Journal on Numerical Analysis", "volume": "55", "number": "2", "publisher": "Society for Industrial and Applied Mathematics", "pagerange": "892-922", "id_number": "CaltechAUTHORS:20170605-100151973", "issn": "0036-1429", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170605-100151973", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "FA9550-15-1-0043" }, { "agency": "NSF", "grant_number": "DMS-1411876" }, { "agency": "National Security Science and Engineering Faculty Fellowship", "grant_number": "N00014-16-1-2808" } ] }, "doi": "10.1137/15M1042279", "primary_object": { "basename": "15m1042279.pdf", "url": "https://authors.library.caltech.edu/records/exker-2rz06/files/15m1042279.pdf" }, "related_objects": [ { "basename": "1509.09213.pdf", "url": "https://authors.library.caltech.edu/records/exker-2rz06/files/1509.09213.pdf" } ], "resource_type": "article", "pub_year": "2017", "author_list": "Bruno, Oscar P. and Cubillos, Max" }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/akmgp-v7f05", "eprint_id": 76841, "eprint_status": "archive", "datestamp": "2023-08-19 01:48:14", "lastmod": "2023-10-25 16:54:54", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar P." }, "orcid": "0000-0001-8369-3014" }, { "id": "Fernandez-Lado-Agustin-G", "name": { "family": "Fernandez-Lado", "given": "Agustin G." } } ] }, "title": "Rapidly convergent quasi-periodic Green functions for scattering by arrays of cylinders\u2014including Wood anomalies", "ispublished": "pub", "full_text_status": "public", "keywords": "Green function, quasi-periodicity,Wood anomaly, grating, scattering", "note": "\u00a9 2017 The Author(s). Published by the Royal Society. \n\nReceived: 26 October 2016; Accepted: 27 January 2017; Published 1 March 2017. \n\nThis work was supported by NSF and AFOSR through contracts DMS-1411876 and FA9550-15-1-0043, and by the NSSEFF Vannevar Bush Fellowship under contract no. N00014-16-1-2808. \n\nThe authors gratefully acknowledge support by NSF and AFOSR as well as the NSSEFF Vannevar Bush Fellowship.\n\nAuthors' contributions: O.P.B. and A.G.F.-L. contributed to all aspects of this article. \n\nNo competing interests exist.\n\nSubmitted - 1610.08567.pdf
", "abstract": "This paper presents a full-spectrum Green-function methodology (which is valid, in particular, at and around Wood-anomaly frequencies) for evaluation of scattering by periodic arrays of cylinders of arbitrary cross section\u2014with application to wire gratings, particle arrays and reflectarrays and, indeed, general arrays of conducting or dielectric bounded obstacles under both transverse electric and transverse magnetic polarized illumination. The proposed method, which, for definiteness, is demonstrated here for arrays of perfectly conducting particles under transverse electric polarization, is based on the use of the shifted Green-function method introduced in a recent contribution (Bruno & Delourme 2014 J. Computat. Phys. 262, 262\u2013290 (doi:10.1016/j.jcp.2013.12.047)). A certain infinite term arises at Wood anomalies for the cylinder-array problems considered here that is not present in the previous rough-surface case. As shown in this paper, these infinite terms can be treated via an application of ideas related to the Woodbury\u2013Sherman\u2013Morrison formulae. The resulting approach, which is applicable to general arrays of obstacles even at and around Wood-anomaly frequencies, exhibits fast convergence and high accuracies. For example, a few hundreds of milliseconds suffice for the proposed approach to evaluate solutions throughout the resonance region (wavelengths comparable to the period and cylinder sizes) with full single-precision accuracy.", "date": "2017-03", "date_type": "published", "publication": "Proceedings of the Royal Society A: Mathematical, physical, and engineering sciences", "volume": "473", "number": "2199", "publisher": "Royal Society of London", "pagerange": "Art. No. 20160802", "id_number": "CaltechAUTHORS:20170424-093441215", "issn": "1364-5021", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170424-093441215", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1411876" }, { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "FA9550-15-1-0043" }, { "agency": "National Security Science and Engineering Faculty Fellowship", "grant_number": "N00014-16-1-2808" } ] }, "doi": "10.1098/rspa.2016.0802", "pmcid": "PMC5378244", "primary_object": { "basename": "1610.08567.pdf", "url": "https://authors.library.caltech.edu/records/akmgp-v7f05/files/1610.08567.pdf" }, "resource_type": "article", "pub_year": "2017", "author_list": "Bruno, Oscar P. and Fernandez-Lado, Agustin G." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/w3sjb-41r38", "eprint_id": 62114, "eprint_status": "archive", "datestamp": "2023-08-20 13:53:34", "lastmod": "2023-10-25 16:51:50", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar P." }, "orcid": "0000-0001-8369-3014" }, { "id": "Lyon-M", "name": { "family": "Lyon", "given": "Mark" } }, { "id": "P\u00e9rez-Arancibia-C", "name": { "family": "P\u00e9rez-Arancibia", "given": "Carlos" }, "orcid": "0000-0003-1647-4019" }, { "id": "Turc-C", "name": { "family": "Turc", "given": "Catalin" } } ] }, "title": "Windowed Green Function method for layered-media scattering", "ispublished": "pub", "full_text_status": "public", "keywords": "Sommerfeld integrals, layered-media scattering, layer Green function", "note": "\u00a9 2016 Society for Industrial and Applied Mathematics. \n\nReceived by the editors August 4, 2015; accepted for publication (in revised form) July 7, 2016; published electronically September 22, 2016. \n\nFunding: The first author's research was supported by the NSF and AFOSR through contracts DMS-1411876 and FA9550-15-1-0043. The fourth author's research was supported by the NSF through contract DMS-1312169.\n\nPublished - 15m1033782.pdf
Submitted - 1507.04445v2.pdf
", "abstract": "This paper introduces a new windowed Green function (WGF) method for the numerical integral-equation solution of problems of electromagnetic scattering by obstacles in the presence of dielectric or conducting half-planes. The WGF method, which is based on the use of smooth windowing functions and integral kernels that can be expressed directly in terms of the free-space Green function, does not require evaluation of expensive Sommerfeld integrals. The proposed approach is fast, accurate, flexible, and easy to implement. In particular, straightforward modifications of existing (accelerated or unaccelerated) integral-equation solvers suffice to incorporate the WGF capability. The method relies on a certain integral equation posed on the union of the boundary of the obstacle and a small flat section of the interface between the penetrable media. Our analysis and numerical experiments demonstrate that both the near- and far-field errors resulting from the proposed approach decrease faster than any negative power of the window size. In the examples considered in this paper the proposed method is up to thousands of times faster, for a given accuracy, than a corresponding method based on use of Sommerfeld integrals.", "date": "2016-09-22", "date_type": "published", "publication": "SIAM Journal on Applied Mathematics", "volume": "76", "number": "5", "publisher": "Society for Industrial and Applied Mathematics", "pagerange": "1871-1898", "id_number": "CaltechAUTHORS:20151116-094725791", "issn": "0036-1399", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20151116-094725791", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1411876" }, { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "FA9550-15-1-0043" }, { "agency": "NSF", "grant_number": "DMS-1312169" } ] }, "doi": "10.1137/15M1033782", "primary_object": { "basename": "1507.04445v2.pdf", "url": "https://authors.library.caltech.edu/records/w3sjb-41r38/files/1507.04445v2.pdf" }, "related_objects": [ { "basename": "15m1033782.pdf", "url": "https://authors.library.caltech.edu/records/w3sjb-41r38/files/15m1033782.pdf" } ], "resource_type": "article", "pub_year": "2016", "author_list": "Bruno, Oscar P.; Lyon, Mark; et el." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/nseem-2am18", "eprint_id": 71113, "eprint_status": "archive", "datestamp": "2023-08-20 12:40:02", "lastmod": "2023-10-23 15:20:33", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar P." }, "orcid": "0000-0001-8369-3014" }, { "id": "Shipman-Stephen-P", "name": { "family": "Shipman", "given": "Stephen P." }, "orcid": "0000-0001-6620-6528" }, { "id": "Turc-Catalin", "name": { "family": "Turc", "given": "Catalin" } }, { "id": "Venakides-Stephanos", "name": { "family": "Venakides", "given": "Stephanos" } } ] }, "title": "Superalgebraically convergent smoothly windowed lattice sums for doubly periodic Green functions in three-dimensional space", "ispublished": "pub", "full_text_status": "public", "keywords": "scatteringperiodic Green functionlattice sumsmooth truncationsuper-algebraic convergenceboundary-integral equations", "note": "\u00a9 2016 The Author(s). Published by the Royal Society. \n\nReceived April 8, 2016. Accepted June 2, 2016. Published 6 July 2016. \n\nThe authors gratefully acknowledge support from AFOSR and NSF under contracts FA9550-15-1-0043 and DMS-1411876 (O.P.B.); NSF DMS-0807325 (S.P.S.); NSF DMS-1008076 (C.T.) and NSF DMS-0707488 and NSF DMS-1211638 (S.V.). \n\nData accessibility: All data applicable to this paper are included in the article. \n\nAuthors' contributions: All authors are equally considered co-contributors in this article. \n\nThere are no competing interests relevant to this article.\n\nSubmitted - 1307.1176.pdf
", "abstract": "This work, part I in a two-part series, presents: (i) a simple and highly efficient algorithm for evaluation of quasi-periodic Green functions, as well as (ii) an associated boundary-integral equation method for the numerical solution of problems of scattering of waves by doubly periodic arrays of scatterers in three-dimensional space. Except for certain 'Wood frequencies' at which the quasi-periodic Green function ceases to exist, the proposed approach, which is based on smooth windowing functions, gives rise to tapered lattice sums which converge superalgebraically fast to the Green function\u2014that is, faster than any power of the number of terms used. This is in sharp contrast to the extremely slow convergence exhibited by the lattice sums in the absence of smooth windowing. (The Wood-frequency problem is treated in part II.) This paper establishes rigorously the superalgebraic convergence of the windowed lattice sums. A variety of numerical results demonstrate the practical efficiency of the proposed approach.", "date": "2016-07", "date_type": "published", "publication": "Proceedings of the Royal Society A: Mathematical, physical, and engineering sciences", "volume": "472", "number": "2191", "publisher": "Royal Society of London", "pagerange": "Art. No. 20160255", "id_number": "CaltechAUTHORS:20161014-131501720", "issn": "1364-5021", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161014-131501720", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "FA9550-15-1-0043" }, { "agency": "NSF", "grant_number": "DMS-1411876" }, { "agency": "NSF", "grant_number": "DMS-0807325" }, { "agency": "NSF", "grant_number": "DMS-1008076" }, { "agency": "NSF", "grant_number": "DMS-0707488" }, { "agency": "NSF", "grant_number": "DMS-1211638" } ] }, "doi": "10.1098/rspa.2016.0255", "pmcid": "PMC4971249", "primary_object": { "basename": "1307.1176.pdf", "url": "https://authors.library.caltech.edu/records/nseem-2am18/files/1307.1176.pdf" }, "resource_type": "article", "pub_year": "2016", "author_list": "Bruno, Oscar P.; Shipman, Stephen P.; et el." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/yhk46-tq141", "eprint_id": 64597, "eprint_status": "archive", "datestamp": "2023-08-19 20:42:17", "lastmod": "2023-10-17 21:32:07", "type": "monograph", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar P." }, "orcid": "0000-0001-8369-3014" }, { "id": "Shipman-S-P", "name": { "family": "Shipman", "given": "Stephen P." }, "orcid": "0000-0001-6620-6528" }, { "id": "Turc-C", "name": { "family": "Turc", "given": "Catalin" } }, { "id": "Venakided-S", "name": { "family": "Venakides", "given": "Stephanos" } } ] }, "title": "Efficient Evaluation of Doubly Periodic Green Functions in 3D Scattering, Including Wood Anomaly Frequencies", "ispublished": "unpub", "full_text_status": "public", "keywords": "scattering, periodic Green function, lattice sum, smooth truncation, Wood\nfrequency, Wood anomaly, boundary-integral equations, electromagnetic computation", "note": "Submitted on 4 Jul 2013. \n\nThis manuscript is a preliminary version of our work, which is made available through arXiv to facilitate rapid dissemination. A more developed text is in preparation.\n\nThis research was supported by grants from NSF and AFOSR (OB) and grants NSF DMS-0807325 (SPS), NSF DMS-1008076 (CT), and NSF DMS-0707488 (SV).\n\nSubmitted - 1307.1176.pdf
", "abstract": "We present effcient methods for computing wave scattering by diffraction gratings that exhibit two-dimensional periodicity in three dimensional (3D) space. Applications include scattering in acoustics, electromagnetics and elasticity. Our approach uses boundary-integral equations.\nThe quasi-periodic Green function employed is structured as a doubly infinite sum of scaled 3D free-space outgoing Helmholtz Green functions. Their source points are located at the nodes of a periodicity lattice of the grating; the scaling is effected by Bloch quasi-periodic coefficients.\nFor efficient numerical computation of the lattice sum, we employ a smooth truncation. Super-algebraic convergence to the Green function is achieved as the truncation radius increases, except at frequency-wavenumber pairs at which a Rayleigh wave is at exactly grazing incidence to the grating. At these \"Wood frequencies\", the term in the Fourier series representation of the Green function that corresponds to the grazing Rayleigh wave acquires an infinite coefficient and the lattice sum blows up. A related challenge occurs at non-exact grazing incidence of a\nRayleigh wave; in this case, the constants in the truncation-error bound become too large. At Wood frequencies, we modify the Green function by adding two types of terms to it. The first type adds weighted spatial shifts of the Green function to itself. The shifts are such that the spatial singularities introduced by these terms are located below the grating and therefore out of the domain of interest. With suitable choices of the weights, these terms annihilate the growing contributions in the original lattice sum and yield algebraic convergence. The degree of the algebraic convergence depends on the number of the added shifts. The second-type terms are quasi-periodic plane wave solutions of the Helmholtz equation. They reinstate (with controlled coeficients now) the grazing modes, effectively eliminated by the terms of first type. These modes are needed in the Green function for guaranteeing the well-posedness of the boundaryintegral\nequation that yields the scattered field. We apply this approach to acoustic scattering by a doubly periodic 2D grating near and at Wood frequencies and scattering by a doubly periodic array of scatterers away from Wood\nfrequencies.", "date": "2016-02-19", "date_type": "published", "id_number": "CaltechAUTHORS:20160219-073954516", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160219-073954516", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Air Force Office of Scientific Research (AFOSR)" }, { "agency": "NSF", "grant_number": "DMS-0807325" }, { "agency": "NSF", "grant_number": "DMS-1008076" }, { "agency": "NSF", "grant_number": "DMS-0707488" } ] }, "doi": "10.48550/arXiv.1307.1176", "primary_object": { "basename": "1307.1176.pdf", "url": "https://authors.library.caltech.edu/records/yhk46-tq141/files/1307.1176.pdf" }, "resource_type": "monograph", "pub_year": "2016", "author_list": "Bruno, Oscar P.; Shipman, Stephen P.; et el." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/m0f47-nhx10", "eprint_id": 90597, "eprint_status": "archive", "datestamp": "2023-08-22 17:23:53", "lastmod": "2023-10-19 14:37:18", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Amlani-F", "name": { "family": "Amlani", "given": "Faisal" } }, { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar P." }, "orcid": "0000-0001-8369-3014" } ] }, "title": "An FC-based spectral solver for elastodynamic problems in general three-dimensional domains", "ispublished": "pub", "full_text_status": "restricted", "keywords": "Elastic wave equation; Spectral solver; General domain; FC solver; Seismic simulations; Non-destructive testing", "note": "\u00a9 2015 Elsevier. \n\nReceived 21 March 2015, Revised 27 November 2015, Accepted 28 November 2015, Available online 8 December 2015. \n\nThe authors gratefully acknowledge support from NSF (Grants DMS-1008631 and DMS-1411876) and AFOSR (Grants FA9550-11-1-0193 and FA9550-15-1-0043). Our interactions with Prof. J. Carlos L\u00f3pez-V\u00e1zquez and his collaborators at the University of Vigo provided one of the main motivations for the efforts leading to the present contribution; we thank these colleagues for profitable discussions and for providing data on through-hole plate-scattering experiments. Valuable conversations with Prof. D. Appelo are also gratefully acknowledged.", "abstract": "This paper presents a spectral numerical algorithm for the solution of elastodynamics problems in general three-dimensional domains. Based on a recently introduced \"Fourier continuation\" (FC) methodology for accurate Fourier expansion of non-periodic functions, the proposed approach possesses a number of appealing properties: it yields results that are essentially free of dispersion errors, it entails mild CFL constraints, it runs at a cost that scales linearly with the discretization sizes, and it lends itself easily to efficient parallelization in distributed-memory computing clusters. The proposed algorithm is demonstrated in this paper by means of a number of applications to problems of isotropic elastodynamics that arise in the fields of materials science and seismology. These examples suggest that the new approach can yield solutions within a prescribed error tolerance by means of significantly smaller discretizations and shorter computing times than those required by other methods.", "date": "2016-02-15", "date_type": "published", "publication": "Journal of Computational Physics", "volume": "307", "publisher": "Elsevier", "pagerange": "333-354", "id_number": "CaltechAUTHORS:20181101-152904690", "issn": "0021-9991", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20181101-152904690", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1008631" }, { "agency": "NSF", "grant_number": "DMS-1411876" }, { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "FA9550-11-1-0193" }, { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "FA9550-15-1-0043" } ] }, "doi": "10.1016/j.jcp.2015.11.060", "resource_type": "article", "pub_year": "2016", "author_list": "Amlani, Faisal and Bruno, Oscar P." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/p9e78-gay76", "eprint_id": 64564, "eprint_status": "archive", "datestamp": "2023-08-22 17:23:34", "lastmod": "2023-10-17 21:30:45", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar P." }, "orcid": "0000-0001-8369-3014" }, { "id": "Cubillos-M", "name": { "family": "Cubillos", "given": "Max" } } ] }, "title": "Higher-order in time \"quasi-unconditionally stable\" ADI solvers for the compressible Navier\u2013Stokes equations in 2D and 3D curvilinear domains", "ispublished": "pub", "full_text_status": "public", "keywords": "Navier\u2013Stokes; Alternating direction implicit; Quasi-unconditional stability; High order", "note": "\u00a9 2015 Elsevier Inc. \n\nReceived 1 October 2015; Received in revised form 20 November 2015; Accepted 2 December 2015; Available online 11 December 2015. \n\nThe authors gratefully acknowledge support from the Air Force Office of Scientific Research and the National Science Foundation. M.C. also thanks the National Physical Science Consortium for their support of this effort.\n\nSubmitted - 1509.09262v1.pdf
", "abstract": "This paper introduces alternating-direction implicit (ADI) solvers of higher order of time-accuracy (orders two to six) for the compressible Navier\u2013Stokes equations in two- and three-dimensional curvilinear domains. The higher-order accuracy in time results from 1) An application of the backward differentiation formulae time-stepping algorithm (BDF) in conjunction with 2) A BDF-like extrapolation technique for certain components of the nonlinear terms (which makes use of nonlinear solves unnecessary), as well as 3) A novel application of the Douglas\u2013Gunn splitting (which greatly facilitates handling of boundary conditions while preserving higher-order accuracy in time). As suggested by our theoretical analysis of the algorithms for a variety of special cases, an extensive set of numerical experiments clearly indicate that all of the BDF-based ADI algorithms proposed in this paper are \"quasi-unconditionally stable\" in the following sense: each algorithm is stable for all couples (h,\u0394t)of spatial and temporal mesh sizes in a problem-dependent rectangular neighborhood of the form (0,M_h)\u00d7(0,M_t). In other words, for each fixed value of \u0394t below a certain threshold, the Navier\u2013Stokes solvers presented in this paper are stable for arbitrarily small spatial mesh-sizes. The second-order formulation has further been rigorously shown to be unconditionally stable for linear hyperbolic and parabolic equations in two-dimensional space. Although implicit ADI solvers for the Navier\u2013Stokes equations with nominal second-order of temporal accuracy have been proposed in the past, the algorithms presented in this paper are the first ADI-based Navier\u2013Stokes solvers for which second-order or better accuracy has been verified in practice under non-trivial (non-periodic) boundary conditions.", "date": "2016-02-15", "date_type": "published", "publication": "Journal of Computational Physics", "volume": "307", "publisher": "Elsevier", "pagerange": "476-495", "id_number": "CaltechAUTHORS:20160218-124347606", "issn": "0021-9991", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160218-124347606", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Air Force Office of Scientific Research (AFOSR)" }, { "agency": "NSF" }, { "agency": "National Physical Science Consortium (NPSC)" } ] }, "doi": "10.1016/j.jcp.2015.12.010", "primary_object": { "basename": "1509.09262v1.pdf", "url": "https://authors.library.caltech.edu/records/p9e78-gay76/files/1509.09262v1.pdf" }, "resource_type": "article", "pub_year": "2016", "author_list": "Bruno, Oscar P. and Cubillos, Max" }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/0h4xf-25e15", "eprint_id": 59813, "eprint_status": "archive", "datestamp": "2023-08-22 16:28:55", "lastmod": "2023-10-23 22:44:52", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Akhmetgaliyev-E", "name": { "family": "Akhmetgaliyev", "given": "Eldar" }, "orcid": "0000-0003-4031-2351" }, { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar P." }, "orcid": "0000-0001-8369-3014" }, { "id": "Nigam-Nilima", "name": { "family": "Nigam", "given": "Nilima" } } ] }, "title": "A boundary integral algorithm for the Laplace Dirichlet-Neumann mixed eigenvalue problem", "ispublished": "pub", "full_text_status": "public", "keywords": "Fourier continuation; Boundary integral operators; Mixed boundary conditions; Zaremba eigenvalue problem; Laplace eigenvalue problem", "note": "\u00a9 2015 Elsevier Inc. \n\nReceived 1 November 2014; Accepted 13 May 2015; Available online 3 June 2015. \n\nE.A. and O.B. gratefully acknowledge support from AFOSR and NSF under contracts FA9550-11-1-0193, FA9550-15-1-0043, DMS-1008631 and DMS-1411876. N.N. gratefully acknowledges support from NSERC and the Canada Research Chairs foundation.\n\nSubmitted - 1411.0071v1.pdf
", "abstract": "We present a novel integral-equation algorithm for evaluation of Zaremba eigenvalues and eigenfunctions, that is, eigenvalues and eigenfunctions of the Laplace operator with mixed Dirichlet\u2013Neumann boundary conditions; of course, (slight modifications of) our algorithms are also applicable to the pure Dirichlet and Neumann eigenproblems. Expressing the eigenfunctions by means of an ansatz based on the single layer boundary operator, the Zaremba eigenproblem is transformed into a nonlinear equation for the eigenvalue \u03bc. For smooth domains the singular structure at Dirichlet\u2013Neumann junctions is incorporated as part of our corresponding numerical algorithm\u2014which otherwise relies on use of the cosine change of variables, trigonometric polynomials and, to avoid the Gibbs phenomenon that would arise from the solution singularities, the Fourier Continuation method (FC). The resulting numerical algorithm converges with high order accuracy without recourse to use of meshes finer than those resulting from the cosine transformation. For non-smooth (Lipschitz) domains, in turn, an alternative algorithm is presented which achieves high-order accuracy on the basis of graded meshes. In either case, smooth or Lipschitz boundary, eigenvalues are evaluated by searching for zero minimal singular values of a suitably stabilized discrete version of the single layer operator mentioned above. (The stabilization technique is used to enable robust non-local zero searches.) The resulting methods, which are fast and highly accurate for high- and low-frequencies alike, can solve extremely challenging two-dimensional Dirichlet, Neumann and Zaremba eigenproblems with high accuracies in short computing times\u2014enabling, in particular, evaluation of thousands of eigenvalues and corresponding eigenfunctions for a given smooth or non-smooth geometry with nearly full double-precision accuracy.", "date": "2015-10-01", "date_type": "published", "publication": "Journal of Computational Physics", "volume": "298", "publisher": "Elsevier", "pagerange": "1-28", "id_number": "CaltechAUTHORS:20150821-120443842", "issn": "0021-9991", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20150821-120443842", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "FA9550-11-1-0193" }, { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "FA9550-15-1-0043" }, { "agency": "NSF", "grant_number": "DMS-1008631" }, { "agency": "NSF", "grant_number": "DMS-1411876" }, { "agency": "Natural Sciences and Engineering Research Council of Canada (NSERC)" }, { "agency": "Canada Research Chairs Program" } ] }, "doi": "10.1016/j.jcp.2015.05.016", "primary_object": { "basename": "1411.0071v1.pdf", "url": "https://authors.library.caltech.edu/records/0h4xf-25e15/files/1411.0071v1.pdf" }, "resource_type": "article", "pub_year": "2015", "author_list": "Akhmetgaliyev, Eldar; Bruno, Oscar P.; et el." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/tz1j9-v6r17", "eprint_id": 58882, "eprint_status": "archive", "datestamp": "2023-08-22 16:13:53", "lastmod": "2023-10-23 19:50:26", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Boubendir-Y", "name": { "family": "Boubendir", "given": "Yassine" } }, { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar" }, "orcid": "0000-0001-8369-3014" }, { "id": "Levadoux-D", "name": { "family": "Levadoux", "given": "David" } }, { "id": "Turc-C", "name": { "family": "Turc", "given": "Catalin" } } ] }, "title": "Integral equations requiring small numbers of Krylov-subspace iterations for two-dimensional smooth penetrable scattering problems", "ispublished": "pub", "full_text_status": "public", "keywords": "Electromagnetic scattering; Transmission problems; Combined field integral equations; Pseudo-differential operators; Regularizing operators", "note": "\u00a9 2015 IMACS. Published by Elsevier B. V.\n\nAvailable online 26 January 2015.\n\nOscar Bruno thanks NSF (contracts DMS-1008631 and DMS-1411876) and AFOSR (contracts FA9550-11-1-0193 and\nFA9550-15-1-0043) for their support during the preparation of this work. Yassine Boubendir gratefully acknowledges support\nfrom NSF through contract DMS-1016405. Catalin Turc gratefully acknowledge support from NSF through contract\nDMS-1008076.\n\nSubmitted - 1310.1416v1.pdf
", "abstract": "This paper presents a class of boundary integral equations for the solution of problems of electromagnetic and acoustic scattering by two-dimensional homogeneous penetrable scatterers with smooth boundaries. The new integral equations, which, as is established in this paper, are uniquely solvable Fredholm equations of the second kind, result from representations of fields as combinations of single and double layer potentials acting on appropriately chosen regularizing operators. As demonstrated in this text by means of a variety of numerical examples (that resulted from a high-order Nystr\u00f6m computational implementation of the new equations), these \"regularized combined equations\" can give rise to important reductions in computational costs, for a given accuracy, over those resulting from previous iterative boundary integral equation solvers for transmission problems.", "date": "2015-09", "date_type": "published", "publication": "Applied Numerical Mathematics", "volume": "95", "publisher": "Elsevier", "pagerange": "82-98", "id_number": "CaltechAUTHORS:20150714-133922935", "issn": "0168-9274", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20150714-133922935", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1008631" }, { "agency": "NSF", "grant_number": "DMS-1411876" }, { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "FA9550-11-1-0193" }, { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "FA9550-15-1-0043" }, { "agency": "NSF", "grant_number": "DMS-1016405" }, { "agency": "NSF", "grant_number": "DMS-1008076" } ] }, "doi": "10.1016/j.apnum.2015.01.005", "primary_object": { "basename": "1310.1416v1.pdf", "url": "https://authors.library.caltech.edu/records/tz1j9-v6r17/files/1310.1416v1.pdf" }, "resource_type": "article", "pub_year": "2015", "author_list": "Boubendir, Yassine; Bruno, Oscar; et el." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/bnwxv-snr41", "eprint_id": 57376, "eprint_status": "archive", "datestamp": "2023-08-20 05:45:25", "lastmod": "2023-10-23 17:20:02", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Lintner-S", "name": { "family": "Lintner", "given": "St\u00e9phane K." } }, { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar P." }, "orcid": "0000-0001-8369-3014" } ] }, "title": "A generalized Calderon formula for open-arc diffraction problems: theoretical considerations", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2015 Royal Society of Edinburgh. Published online: 02 April 2015. MS received 19 April 2012; accepted 10 January 2014.\n\nThe authors gratefully acknowledge support from the National Science Foundation and the Air Force Office of Scientific Research.\n\nSubmitted - 1204.3699v2.pdf
", "abstract": "We deal with the general problem of scattering by open arcs in two-dimensional space. We show that this problem can be solved by means of certain second-kind integral equations of the form \u00d1S[\u03c6] = \u0192, where \u00d1 and S are first-kind integral operators whose composition gives rise to a generalized Calder\u00f3n formula of the form \u00d1S = J^\u03c4_0 + K in a weighted, periodized Sobolev space. (Here J^\u03c4_0 is a continuous and continuously invertible operator and K is a compact operator.) The \u00d1S formulation provides, for the first time, a second-kind integral equation for the open-arc scattering problem with Neumann boundary conditions. Numerical experiments show that, for both the Dirichlet and Neumann boundary conditions, our second-kind integral equations have spectra that are bounded away from zero and infinity as k \u2192 \u221e; to the authors' knowledge these are the first integral equations for these problems that possess this desirable property. This situation is in stark contrast with that arising from the related classical open-surface hypersingular and single-layer operators N and S, whose composition NS maps, for example, the function \u03d5 = 1 into a function that is not even square integrable. Our proofs rely on three main elements: algebraic manipulations enabled by the presence of integral weights; use of the classical result of continuity of the Ces\u00e0ro operator; and explicit characterization of the point spectrum of J^\u03c4_0, which, interestingly, can be decomposed into the union of a countable set and an open set, both of which are tightly clustered around -1/4. As shown in a separate contribution, the new approach can be used to construct simple, spectrally accurate numerical solvers and, when used in conjunction with Krylov-subspace iterative solvers such as the generalized minimal residual method, it gives rise to a dramatic reduction in the number of iterations compared with those required by other approaches.", "date": "2015-04-03", "date_type": "published", "publication": "Proceedings of the Royal Society of Edinburgh: Section A Mathematics", "volume": "145", "number": "2", "publisher": "Royal Society of Edinburgh", "pagerange": "331-364", "id_number": "CaltechAUTHORS:20150508-105226858", "issn": "0308-2105", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20150508-105226858", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF" }, { "agency": "Air Force Office of Scientific Research (AFOSR)" } ] }, "doi": "10.1017/S0308210512000807", "primary_object": { "basename": "1204.3699v2.pdf", "url": "https://authors.library.caltech.edu/records/bnwxv-snr41/files/1204.3699v2.pdf" }, "resource_type": "article", "pub_year": "2015", "author_list": "Lintner, St\u00e9phane K. and Bruno, Oscar P." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/gszt6-dmh33", "eprint_id": 67508, "eprint_status": "archive", "datestamp": "2023-08-20 04:15:15", "lastmod": "2023-10-18 21:14:56", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar P." }, "orcid": "0000-0001-8369-3014" }, { "id": "Elling-T", "name": { "family": "Elling", "given": "Timothy" } }, { "id": "Sen-A", "name": { "family": "Sen", "given": "Ayon" } } ] }, "title": "A Fourier Continuation Method for the Solution of Elliptic Eigenvalue Problems in General Domains", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2015 Oscar P. Bruno et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. \n\nReceived 2 July 2015; Accepted 25 October 2015. \n\nThe authors declare that there is no conflict of interests regarding the publication of this paper. \n\nThe authors gratefully acknowledge support from NSF and AFOSR.\n\nPublished - 184786.pdf
", "abstract": "We present a new computational method for the solution of elliptic eigenvalue problems with variable coefficients in general two-dimensional domains. The proposed approach is based on use of the novel Fourier continuation method (which enables fast and highly accurate Fourier approximation of nonperiodic functions in equispaced grids without the limitations arising from the Gibbs phenomenon) in conjunction with an overlapping patch domain decomposition strategy and Arnoldi iteration. A variety of examples demonstrate the versatility, accuracy, and generality of the proposed methodology.", "date": "2015", "date_type": "published", "publication": "Mathematical Problems in Engineering", "volume": "2015", "publisher": "Hindawi Publishing Corporation", "pagerange": "Art. No. 184786", "id_number": "CaltechAUTHORS:20160531-155956642", "issn": "1024-123X", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160531-155956642", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF" }, { "agency": "Air Force Office of Scientific Research (AFOSR)" } ] }, "doi": "10.1155/2015/184786", "primary_object": { "basename": "184786.pdf", "url": "https://authors.library.caltech.edu/records/gszt6-dmh33/files/184786.pdf" }, "resource_type": "article", "pub_year": "2015", "author_list": "Bruno, Oscar P.; Elling, Timothy; et el." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/a9b6s-m1c92", "eprint_id": 51363, "eprint_status": "archive", "datestamp": "2023-08-20 03:03:13", "lastmod": "2023-10-18 16:19:16", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "P\u00e9rez-Arancibia-C", "name": { "family": "P\u00e9rez-Arancibia", "given": "Carlos" }, "orcid": "0000-0003-1647-4019" }, { "id": "Zhang-Peng", "name": { "family": "Zhang", "given": "Peng" } }, { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar P." }, "orcid": "0000-0001-8369-3014" }, { "id": "Lau-Y-Y", "name": { "family": "Lau", "given": "Y. Y." } } ] }, "title": "Electromagnetic power absorption due to bumps and trenches on flat surfaces", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2014 AIP Publishing LLC.\n\nReceived 14 July 2014; accepted 12 September 2014; published online 26 September 2014.\n\nThis Caltech-Michigan collaboration was stimulated by\ndiscussions with Dr. Arje Nachman and Dr. John Luginsland\nof the Air Force Office of Scientific Research. The Caltech\ngroup was supported by AFOSR and NSF under Contract\nNos. FA9550-11-1-0193 and DMS-1008631, respectively.\nThe University of Michigan group was supported by AFOSR\ngrants FA9550-09-1-0662, FA9550-14-1-0309, and L-3\nCommunication Electron Devices Division.\n\nPublished - 1.4896361.pdf
", "abstract": "This paper presents a study of the absorption of electromagnetic power that results from the interaction of electromagnetic waves and cylindrical bumps or trenches on flat conducting surfaces. Configurations are characterized by means of adequately selected dimensionless variables and parameters so that applicability to mathematically equivalent (but physically diverse) systems can be achieved easily. Electromagnetic fields and absorption increments caused by such surface defects are evaluated by means of a high-order integral equation method which resolves fine details of the field near the surface, and which was validated by fully analytical approaches in a range of computationally challenging cases. The computational method is also applied to problems concerning bumps and trenches on imperfect conducting planes for which analytical solutions are not available. Typically, we find that absorption is enhanced by the presence of the defects considered, although, interestingly, absorption can also be significantly reduced in some cases\u2014such as, e.g., in the case of a trench on a conducting plane where the incident electric field is perpendicular to the plane. Additionally, it is observed that, for some small-skin-depths large-wavelengths, the absorption increment is proportional to the increase in surface area. Significant physical insight is obtained on the heating that results from various types of electromagnetic incident fields.", "date": "2014-09-28", "date_type": "published", "publication": "Journal of Applied Physics", "volume": "116", "number": "12", "publisher": "American Institute of Physics", "pagerange": "Art. No. 124904", "id_number": "CaltechAUTHORS:20141106-103044717", "issn": "0021-8979", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20141106-103044717", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "FA9550-11-1-0193" }, { "agency": "NSF", "grant_number": "DMS-1008631" }, { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "FA9550-09-1-0662" }, { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "FA9550-14-1-0309" }, { "agency": "L-3 Communication Electron Devices Division" } ] }, "doi": "10.1063/1.4896361", "primary_object": { "basename": "1.4896361.pdf", "url": "https://authors.library.caltech.edu/records/a9b6s-m1c92/files/1.4896361.pdf" }, "resource_type": "article", "pub_year": "2014", "author_list": "P\u00e9rez-Arancibia, Carlos; Zhang, Peng; et el." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/yw26a-66z29", "eprint_id": 50303, "eprint_status": "archive", "datestamp": "2023-08-20 02:18:54", "lastmod": "2023-10-17 22:54:59", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "P\u00e9rez-Arancibia-C", "name": { "family": "P\u00e9rez-Arancibia", "given": "Carlos" }, "orcid": "0000-0003-1647-4019" }, { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar P." }, "orcid": "0000-0001-8369-3014" } ] }, "title": "High-order integral equation methods for problems of scattering by bumps and cavities on half-planes", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2014 Optical Society of America.\n\nReceived May 19, 2014; accepted June 17, 2014; posted June 20, 2014 (Doc. ID 212305); published July 15, 2014.\n\nThe authors gratefully acknowledge support from the Air\nForce Office of Scientific Research and the National Science\nFoundation.\n\nPublished - josaa-31-8-1738.pdf
Submitted - 1405.4336v1.pdf
", "abstract": "This paper presents high-order integral equation methods for the evaluation of electromagnetic wave scattering by dielectric bumps and dielectric cavities on perfectly conducting or dielectric half-planes. In detail, the algorithms introduced in this paper apply to eight classical scattering problems, namely, scattering by a dielectric bump on a perfectly conducting or a dielectric half-plane, and scattering by a filled, overfilled, or void dielectric cavity on a perfectly conducting or a dielectric half-plane. In all cases field representations based on single-layer potentials for appropriately chosen Green functions are used. The numerical far fields and near fields exhibit excellent convergence as discretizations are refined\u2014even at and around points where singular fields and infinite currents exist.", "date": "2014-08", "date_type": "published", "publication": "Journal of the Optical Society of America A", "volume": "31", "number": "8", "publisher": "Optical Society of America", "pagerange": "1738-1746", "id_number": "CaltechAUTHORS:20141009-095915180", "issn": "1084-7529", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20141009-095915180", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Air Force Office of Scientific Research (AFOSR)" }, { "agency": "NSF" } ] }, "doi": "10.1364/JOSAA.31.001738", "primary_object": { "basename": "josaa-31-8-1738.pdf", "url": "https://authors.library.caltech.edu/records/yw26a-66z29/files/josaa-31-8-1738.pdf" }, "related_objects": [ { "basename": "1405.4336v1.pdf", "url": "https://authors.library.caltech.edu/records/yw26a-66z29/files/1405.4336v1.pdf" } ], "resource_type": "article", "pub_year": "2014", "author_list": "P\u00e9rez-Arancibia, Carlos and Bruno, Oscar P." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/4qfka-asg90", "eprint_id": 46234, "eprint_status": "archive", "datestamp": "2023-08-20 01:07:06", "lastmod": "2023-10-26 19:36:26", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar P." }, "orcid": "0000-0001-8369-3014" }, { "id": "Jimenez-E", "name": { "family": "Jimenez", "given": "Edwin" } } ] }, "title": "Higher-Order Linear-Time Unconditionally Stable Alternating Direction Implicit Methods for Nonlinear Convection-Diffusion Partial Differential Equation Systems", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2014 by ASME.\n\nContributed by the Fluids Engineering Division of ASME for publication in the Journal of Fluids Engineering.\nManuscript received December 2, 2013; final\nmanuscript received January 29, 2014; published online April 28, 2014. Assoc.\nEditor: Ye Zhou.\n\nThe authors gratefully acknowledge support by the Air Force\nOffice of Scientific Research and the National Science Foundation.\nWe are also thankful for a number of useful comments from\nthe reviewers, which have helped improve the quality of this\npresentation.\n\nPublished - fe_136_06_060904.pdf
", "abstract": "We introduce a class of alternating direction implicit (ADI) methods, based on approximate factorizations of backward differentiation formulas (BDFs) of order p\u22652, for the numerical solution of two-dimensional, time-dependent, nonlinear, convection-diffusion partial differential equation (PDE) systems in Cartesian domains. The proposed algorithms, which do not require the solution of nonlinear systems, additionally produce solutions of spectral accuracy in space through the use of Chebyshev approximations. In particular, these methods give rise to minimal artificial dispersion and diffusion and they therefore enable use of relatively coarse discretizations to meet a prescribed error tolerance for a given problem. A variety of numerical results presented in this text demonstrate high-order accuracy and, for the particular cases of p=2,3, unconditional stability.", "date": "2014-06", "date_type": "published", "publication": "Journal of Fluids Engineering", "volume": "136", "number": "6", "publisher": "American Society of Mechanical Engineers", "pagerange": "Art. No. 060904", "id_number": "CaltechAUTHORS:20140612-100139439", "issn": "0098-2202", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20140612-100139439", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Air Force Office of Scientific Research (AFOSR)" }, { "agency": "NSF" } ] }, "doi": "10.1115/1.4026868", "primary_object": { "basename": "fe_136_06_060904.pdf", "url": "https://authors.library.caltech.edu/records/4qfka-asg90/files/fe_136_06_060904.pdf" }, "resource_type": "article", "pub_year": "2014", "author_list": "Bruno, Oscar P. and Jimenez, Edwin" }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/d1qvs-apt45", "eprint_id": 44290, "eprint_status": "archive", "datestamp": "2023-08-22 12:24:16", "lastmod": "2023-10-26 00:22:09", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar P." }, "orcid": "0000-0001-8369-3014" }, { "id": "Delourme-B", "name": { "family": "Delourme", "given": "B\u00e9rang\u00e8re" } } ] }, "title": "Rapidly convergent two-dimensional quasi-periodic Green function throughout the spectrum-including Wood anomalies", "ispublished": "pub", "full_text_status": "restricted", "keywords": "Wood anomaly; Quasi-periodic Green function; Rough-surface scattering; Diffraction grating; Ewald summation method; Scattering by periodic surfaces; Lattice sums; Time-harmonic Helmholtz equation; Time-harmonic Maxwell equations; Integral equation methods; Boundary integral methods", "note": "\u00a9 2013 Elsevier Inc. Received 15 October 2013. Received in revised form 20 December 2013. Accepted 23 December 2013.\nAvailable online 9 January 2014. The authors thank Dr. Santiago Fortes for his assistance during the preliminary phases of this project. Support from NSF and AFOSR is gratefully acknowledged.", "abstract": "We introduce a new methodology, based on new quasi-periodic Green functions which converge rapidly even at and around Wood-anomaly configurations, for the numerical solution of problems of scattering by periodic rough surfaces in two-dimensional space. As is well known the classical quasi-periodic Green function ceases to exist at Wood anomalies. The approach introduced in this text produces fast Green function convergence throughout the spectrum on the basis of a certain \"finite-differencing\" approach and smooth windowing of the classical Green function lattice sum. The resulting Green-function convergence is super-algebraically fast away from Wood anomalies, and it reduces to an arbitrarily-high (user-prescribed) algebraic order of convergence at Wood anomalies.", "date": "2014-04-01", "date_type": "published", "publication": "Journal of Computational Physics", "volume": "262", "publisher": "Elsevier", "pagerange": "262-290", "id_number": "CaltechAUTHORS:20140313-090333919", "issn": "0021-9991", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20140313-090333919", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF" }, { "agency": "Air Force Office of Scientific Research (AFOSR)" } ] }, "doi": "10.1016/j.jcp.2013.12.047", "resource_type": "article", "pub_year": "2014", "author_list": "Bruno, Oscar P. and Delourme, B\u00e9rang\u00e8re" }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/gqr3p-4x754", "eprint_id": 43850, "eprint_status": "archive", "datestamp": "2023-08-22 11:35:44", "lastmod": "2023-10-25 23:56:37", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "O. P." }, "orcid": "0000-0001-8369-3014" }, { "id": "Prieto-A", "name": { "family": "Prieto", "given": "A." } } ] }, "title": "Spatially Dispersionless, Unconditionally Stable FC\u2013AD\n Solvers for Variable-Coefficient PDEs", "ispublished": "pub", "full_text_status": "public", "keywords": "High-order methods; Alternating Direction Implicit schemes; Numerical dispersion; Variable coefficient problems", "note": "\u00a9 2013 Springer Science+Business Media New York. \n\nReceived: 4 September 2012. Revised: 8 May 2013. Accepted: 13 May 2013. Published online: 5 June 2013. \n\nThe authors gratefully acknowledge support from NSF and AFOSR. The work of A. Prieto was partially supported by Ministerio de Educaci\u00f3n y Ciencia of Spain under project grant MTM2008-02483, programme Angeles Alvari\u00f1o (grant 2007/AA-076) and programme Juan de la Cierva (grant JCI-2010-06793).\n\nSubmitted - 1209.0751v1.pdf
Supplemental Material - 10915_2013_9734_MOESM1_ESM.zip
", "abstract": "We present fast, spatially dispersionless and unconditionally stable high-order solvers for partial differential equations (PDEs) with variable coefficients in general smooth domains. Our solvers, which are based on (i) A certain \"Fourier continuation\" (FC) method for the resolution of the Gibbs phenomenon on equi-spaced Cartesian grids, together with (ii) A new, preconditioned, FC-based solver for two-point boundary value problems for variable-coefficient Ordinary Differential Equations, and (iii) An Alternating Direction strategy, generalize significantly a class of FC-based solvers introduced recently for constant-coefficient PDEs. The present algorithms, which are applicable, with high-order accuracy, to variable-coefficient elliptic, parabolic and hyperbolic PDEs in general domains with smooth boundaries, are unconditionally stable, do not suffer from spatial numerical dispersion, and they run at Fast Fourier Transform speeds. The accuracy, efficiency and overall capabilities of our methods are demonstrated by means of applications to challenging problems of diffusion and wave propagation in heterogeneous media.", "date": "2014-02", "date_type": "published", "publication": "Journal of Scientific Computing", "volume": "58", "number": "2", "publisher": "Springer Verlag", "pagerange": "331-366", "id_number": "CaltechAUTHORS:20140218-114756940", "issn": "0885-7474", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20140218-114756940", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF" }, { "agency": "Air Force Office of Scientific Research (AFOSR)" }, { "agency": "Ministerio de Educaci\u03ccn y Ciencia (MEC)", "grant_number": "MTM2008-02483" }, { "agency": "Angeles Alvari\u00f1o programme", "grant_number": "2007/AA-076" }, { "agency": "Juan de la Cierva programme", "grant_number": "JCI-2010-06793" } ] }, "doi": "10.1007/s10915-013-9734-8", "primary_object": { "basename": "10915_2013_9734_MOESM1_ESM.zip", "url": "https://authors.library.caltech.edu/records/gqr3p-4x754/files/10915_2013_9734_MOESM1_ESM.zip" }, "related_objects": [ { "basename": "1209.0751v1.pdf", "url": "https://authors.library.caltech.edu/records/gqr3p-4x754/files/1209.0751v1.pdf" } ], "resource_type": "article", "pub_year": "2014", "author_list": "Bruno, O. P. and Prieto, A." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/kb4hv-mqk60", "eprint_id": 40998, "eprint_status": "archive", "datestamp": "2023-08-22 10:48:26", "lastmod": "2023-10-24 23:22:05", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar P." }, "orcid": "0000-0001-8369-3014" }, { "id": "Lintner-S-K", "name": { "family": "Lintner", "given": "St\u00e9phane K." } } ] }, "title": "A high-order integral solver for scalar problems of diffraction by screens and apertures in three-dimensional space", "ispublished": "pub", "full_text_status": "public", "keywords": "Open-surface scattering; Integral equation methods; Calderon formula; High-order integral equation methods; Scattering by a disc; Diffraction by an aperture", "note": "\u00a9 2013 Elsevier Inc. \n\nReceived 13 September 2012; Received in revised form 14 June 2013; Accepted 19 June 2013; Available online 1 July 2013. \n\nThe authors gratefully acknowledge support from AFOSR, NSF, JPL and the Betty and Gordon Moore Foundation.\n\nSubmitted - 1208.5173.pdf
", "abstract": "We present a novel methodology for the numerical solution of problems of diffraction by infinitely thin screens in three-dimensional space. Our approach relies on new integral formulations as well as associated high-order quadrature rules. The new integral formulations involve weighted versions of the classical integral operators related to the thin-screen Dirichlet and Neumann problems as well as a generalization to the open-surface problem of the classical Calder\u00f3n formulae. The high-order quadrature rules we introduce for these operators, in turn, resolve the multiple Green function and edge singularities (which occur at arbitrarily close distances from each other, and which include weakly singular as well as hypersingular kernels) and thus give rise to super-algebraically fast convergence as the discretization sizes are increased. When used in conjunction with Krylov-subspace linear algebra solvers such as GMRES, the resulting solvers produce results of high accuracy in small numbers of iterations for low and high frequencies alike. We demonstrate our methodology with a variety of numerical results for screen and aperture problems at high frequencies\u2014including simulation of classical experiments such as the diffraction by a circular disc (featuring in particular the famous Poisson spot), evaluation of interference fringes resulting from diffraction across two nearby circular apertures, as well as solution of problems of scattering by more complex geometries consisting of multiple scatterers and cavities.", "date": "2013-11-01", "date_type": "published", "publication": "Journal of Computational Physics", "volume": "252", "publisher": "Elsevier", "pagerange": "250-274", "id_number": "CaltechAUTHORS:20130829-141339834", "issn": "0021-9991", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130829-141339834", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Air Force Office of Scientific Research (AFOSR)" }, { "agency": "NSF" }, { "agency": "JPL" }, { "agency": "Gordon and Betty Moore Foundation" } ] }, "doi": "10.1016/j.jcp.2013.06.022", "primary_object": { "basename": "1208.5173.pdf", "url": "https://authors.library.caltech.edu/records/kb4hv-mqk60/files/1208.5173.pdf" }, "resource_type": "article", "pub_year": "2013", "author_list": "Bruno, Oscar P. and Lintner, St\u00e9phane K." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/2e6cb-7hq43", "eprint_id": 40708, "eprint_status": "archive", "datestamp": "2023-08-19 20:54:01", "lastmod": "2023-10-24 17:20:27", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar P." }, "orcid": "0000-0001-8369-3014" }, { "id": "Dom\u00ednguez-V", "name": { "family": "Dom\u00ednguez", "given": "V\u00edctor" } }, { "id": "Sayas-F-J", "name": { "family": "Sayas", "given": "Francisco-Javier" } } ] }, "title": "Convergence analysis of a high-order Nystr\u00f6m integral-equation method for surface scattering problems", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2013 Springer-Verlag Berlin Heidelberg. \n\nReceived: 27 September 2011; Revised: 8 July 2012; Published online: 6 March 2013. \n\nOB gratefully acknowledges support from AFOSR and NSF. VD is partially supported by Project MTM2010-21037. FJS is partially supported by the NSF-DMS 1216356 grant. A portion of this research was carried out when FJS was visiting professor at the University of Minnesota and during short visits of FJS and VD to the California Institute of Technology.\n\nSubmitted - 1109.6352v2.pdf
", "abstract": "In this paper we present a convergence analysis for the Nystr\u00f6m method\nproposed in [J Comput Phys 169 (1):80\u2013110, 2001] for the solution of the combined\nboundary integral equation formulations of sound-soft acoustic scattering problems\nin three-dimensional space. This fast and efficient scheme combines FFT techniques\nand a polar change of variables that cancels out the kernel singularity. We establish\nthe stability of the algorithms in the L^2 norm and we derive convergence estimates\nin both the L^2 and L^\u221e norms. In particular, our analysis establishes theoretically the\npreviously observed super-algebraic convergence of the method in cases in which the\nright-hand side is smooth.", "date": "2013-08", "date_type": "published", "publication": "Numerische Mathematik", "volume": "124", "number": "4", "publisher": "Springer", "pagerange": "603-645", "id_number": "CaltechAUTHORS:20130816-112500114", "issn": "0029-599X", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130816-112500114", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Air Force Office of Scientific Research (AFOSR)" }, { "agency": "Ministerio de Ciencia e Innovaci\u00f3n (MICINN)", "grant_number": "MTM2010-21037" }, { "agency": "NSF", "grant_number": "DMS-1216356" } ] }, "doi": "10.1007/s00211-013-0525-9", "primary_object": { "basename": "1109.6352v2.pdf", "url": "https://authors.library.caltech.edu/records/2e6cb-7hq43/files/1109.6352v2.pdf" }, "resource_type": "article", "pub_year": "2013", "author_list": "Bruno, Oscar P.; Dom\u00ednguez, V\u00edctor; et el." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/1p9kh-epw36", "eprint_id": 36402, "eprint_status": "archive", "datestamp": "2023-08-22 07:56:42", "lastmod": "2023-10-20 23:07:06", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar P." }, "orcid": "0000-0001-8369-3014" }, { "id": "Lintner-S", "name": { "family": "Lintner", "given": "St\u00e9phane K." } } ] }, "title": "Second-kind integral solvers for TE and TM problems of diffraction by open arcs", "ispublished": "pub", "full_text_status": "public", "keywords": "diffraction by arcs; electromagnetic scattering; integral solvers; open surface scattering; regularized equations; second-kind dquations", "note": "\u00a9 2012 American Geophysical Union. \n\nReceived 19 April 2012; revised 30 August 2012; accepted 17 September 2012; published 14 December 2012. \n\nThe authors gratefully acknowledge support from AFOSR, NSF, JPL and the Betty and Gordon Moore Foundation.\n\nPublished - rds6037.pdf
Submitted - 1204.3701.pdf
", "abstract": "We present a novel approach for the numerical solution of problems of diffraction\nby open arcs in two dimensional space. Our methodology relies on composition\nof weighted versions of the classical integral operators associated with the Dirichlet\nand Neumann problems (TE and TM polarizations, respectively) together with a\ngeneralization to the open-arc case of the well known closed-surface Calder\u00f3n\nformulae. When used in conjunction with spectrally accurate discretization rules\nand Krylov-subspace linear algebra solvers such as GMRES, the new second-kind\nTE and TM formulations for open arcs produce results of high accuracy in small\nnumbers of iterations\u2014for low and high frequencies alike.", "date": "2012-12-14", "date_type": "published", "publication": "Radio Science", "volume": "47", "number": "6", "publisher": "American Geophysical Union", "pagerange": "Art. No. RS6006", "id_number": "CaltechAUTHORS:20130115-143636940", "issn": "0048-6604", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130115-143636940", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Air Force Office of Scientific Research (AFOSR)" }, { "agency": "NSF" }, { "agency": "JPL" }, { "agency": "Gordon and Betty Moore Foundation" } ] }, "doi": "10.1029/2012RS005035", "primary_object": { "basename": "1204.3701.pdf", "url": "https://authors.library.caltech.edu/records/1p9kh-epw36/files/1204.3701.pdf" }, "related_objects": [ { "basename": "rds6037.pdf", "url": "https://authors.library.caltech.edu/records/1p9kh-epw36/files/rds6037.pdf" } ], "resource_type": "article", "pub_year": "2012", "author_list": "Bruno, Oscar P. and Lintner, St\u00e9phane K." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/dk7wp-s6d42", "eprint_id": 36143, "eprint_status": "archive", "datestamp": "2023-08-19 13:00:33", "lastmod": "2023-10-20 22:17:26", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Albin-N", "name": { "family": "Albin", "given": "Nathan" } }, { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar P." }, "orcid": "0000-0001-8369-3014" }, { "id": "Cheung-T-Y", "name": { "family": "Cheung", "given": "Theresa Y." } }, { "id": "Cleveland-R-O", "name": { "family": "Cleveland", "given": "Robin O." } } ] }, "title": "Fourier continuation methods for high-fidelity simulation of nonlinear acoustic beams", "ispublished": "pub", "full_text_status": "public", "keywords": "acoustic wave scattering, biomedical ultrasonics, finite difference methods, finite element analysis, finite volume methods, Fourier analysis, nonlinear acoustics, partial differential equations", "note": "\u00a9 2012 Acoustical Society of America.\nReceived 12 November 2010; revised 25 May 2012; accepted 12 July 2012.\n\nN.A. gratefully acknowledges the support of the NSF\npostdoctoral fellowship. N.A. and O.P.B. gratefully acknowledge\nsupport from NSF and AFOSR. T.Y.C. and R.O.C.\ngratefully acknowledge support from NSF through grant\n0835795.\n\nPublished - JAS002371.pdf
", "abstract": "On the basis of recently developed Fourier continuation (FC) methods and associated efficient parallelization techniques, this text introduces numerical algorithms that, due to very low dispersive errors, can accurately and efficiently solve the types of nonlinear partial differential equation (PDE) models of nonlinear acoustics in hundred-wavelength domains as arise in the simulation of focused medical ultrasound. As demonstrated in the examples presented in this text, the FC approach can be used to produce solutions to nonlinear acoustics PDEs models with significantly reduced discretization requirements over those associated with finite-difference, finite-element and finite-volume methods, especially in cases involving waves that travel distances that are orders of magnitude longer than their respective wavelengths. In these examples, the FC methodology is shown to lead to improvements in computing times by factors of hundreds and even thousands over those required by the standard approaches. A variety of one-and two-dimensional examples presented in this text demonstrate the power and capabilities of the proposed methodology, including an example containing a number of scattering centers and nonlinear multiple-scattering events.", "date": "2012-10", "date_type": "published", "publication": "Journal of the Acoustical Society of America", "volume": "132", "number": "4", "publisher": "Acoustical Society of America", "pagerange": "2371-2387", "id_number": "CaltechAUTHORS:20130103-105523405", "issn": "0001-4966", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130103-105523405", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF Postdoctoral Fellowship" }, { "agency": "NSF" }, { "agency": "Air Force Office of Scientific Research (AFOSR)" }, { "agency": "NSF", "grant_number": "0835795" } ] }, "doi": "10.1121/1.4742722", "primary_object": { "basename": "JAS002371.pdf", "url": "https://authors.library.caltech.edu/records/dk7wp-s6d42/files/JAS002371.pdf" }, "resource_type": "article", "pub_year": "2012", "author_list": "Albin, Nathan; Bruno, Oscar P.; et el." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/gr4y3-yze09", "eprint_id": 34520, "eprint_status": "archive", "datestamp": "2023-08-22 06:51:00", "lastmod": "2023-10-19 20:42:27", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar" }, "orcid": "0000-0001-8369-3014" }, { "id": "Elling-T", "name": { "family": "Elling", "given": "Tim" } }, { "id": "Turc-C", "name": { "family": "Turc", "given": "Catalin" } } ] }, "title": "Regularized integral equations and fast high-order solvers for sound-hard acoustic scattering problems", "ispublished": "pub", "full_text_status": "public", "keywords": "acoustic scattering; combined field integral equations; pseudo-differential operators", "note": "\u00a9 2012 John Wiley & Sons, Ltd.\n\nReceived 13 July 2011; Revised 25 January 2012; Accepted 26 January 2012.\n\nThe authors gratefully acknowledge support from NSF and AFOSR.\n\nSubmitted - 1508.03438v1.pdf
", "abstract": "This text introduces the following: (1) new regularized combined field integral equations (CFIE-R) for frequency-domain sound-hard scattering problems; and (2) fast, high-order algorithms for the numerical solution of the CFIE-R and related integral equations. Similar to the classical combined field integral equation (CFIE), the CFIE-R are uniquely-solvable integral equations based on the use of single and double layer potentials. Unlike the CFIE, however, the CFIE-R utilize a composition of the double-layer potential with a regularizing operator that gives rise to highly favorable spectral properties\u2014thus making it possible to produce accurate solutions by means of iterative solvers in small numbers of iterations. The CFIE-R-based fast high-order integral algorithms introduced in this text enable highly accurate solution of challenging sound-hard scattering problems, including hundred-wavelength cases, in single-processor runs on present-day desktop computers. A variety of numerical results demonstrate the qualities of the numerical solvers as well as the advantages that arise from the new integral equation formulation.", "date": "2012-09-07", "date_type": "published", "publication": "International Journal for Numerical Methods in Engineering", "volume": "91", "number": "10", "publisher": "John Wiley & Sons", "pagerange": "1045-1072", "id_number": "CaltechAUTHORS:20120927-133224529", "issn": "0029-5981", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20120927-133224529", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF" }, { "agency": "Air Force Office of Scientific Research (AFOSR)" } ] }, "doi": "10.1002/nme.4302", "primary_object": { "basename": "1508.03438v1.pdf", "url": "https://authors.library.caltech.edu/records/gr4y3-yze09/files/1508.03438v1.pdf" }, "resource_type": "article", "pub_year": "2012", "author_list": "Bruno, Oscar; Elling, Tim; et el." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/4cmet-mbn29", "eprint_id": 35792, "eprint_status": "archive", "datestamp": "2023-08-19 11:24:33", "lastmod": "2023-10-20 21:08:58", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "O." }, "orcid": "0000-0001-8369-3014" }, { "id": "Hoch-D", "name": { "family": "Hoch", "given": "D." } } ] }, "title": "Numerical Differentiation of Approximated Functions with Limited Order-of-Accuracy Deterioration", "ispublished": "pub", "full_text_status": "public", "keywords": "numerical differentiation, Chebyshev approximation, differentiation of approximated functions", "note": "\u00a9 2012 Society for Industrial and Applied Mathematics. Submitted: 18 August 2010. Accepted: 21 February 2012.\nPublished online: 19 June 2012. This work was supported by the Air Force Office of Scientific Research and the National Science Foundation.\n\nPublished - 100805807.pdf
", "abstract": "We consider the problem of numerical differentiation of a function f from approximate or noisy values of f on a discrete set of points; such discrete approximate data may result from a numerical calculation (such as a finite element or finite difference solution of a partial differential equation), from experimental measurements, or, generally, from an estimate of some sort. In some such cases it is useful to guarantee that orders of accuracy are not degraded: assuming the approximating values of the function are known with an accuracy of order O(h^r), where h is the mesh size, an accuracy of O(h^r) is desired in the value of the derivatives of f. Differentiation of interpolating polynomials does not achieve this goal since, as shown in this text, n-fold differentiation of an interpolating polynomial of any degree \u2265 (r \u2212 1) obtained from function values containing errors of order O(h^r) generally gives rise to derivative errors of order O(h^(r\u2212n)); other existing differentiation algorithms suffer from similar degradations in the order of accuracy. In this paper we present a new algorithm, the LDC method (low degree Chebyshev), which, using noisy function values of a function f on a (possibly irregular) grid, produces approximate values of derivatives f^((n)) (n = 1, 2 . . .) with limited loss in the order of accuracy. For example, for (possibly nonsmooth) O(h^r) errors in the values of an underlying infinitely differentiable function, the LDC loss in the order of accuracy is \"vanishingly small\": derivatives of smooth functions are approximated by the LDC algorithm with an accuracy of order O(h^r) for all r' < r. The algorithm is very fast and simple; a variety of numerical results we present illustrate the theory and demonstrate the efficiency of the proposed methodology.", "date": "2012-06-19", "date_type": "published", "publication": "SIAM Journal on Numerical Analysis", "volume": "50", "number": "3", "publisher": "Society for Industrial and Applied Mathematics", "pagerange": "1581-1603", "id_number": "CaltechAUTHORS:20121204-113815559", "issn": "0036-1429", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20121204-113815559", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Air Force Office of Scientific Research (AFOSR)" }, { "agency": "NSF" } ] }, "doi": "10.1137/100805807", "primary_object": { "basename": "100805807.pdf", "url": "https://authors.library.caltech.edu/records/4cmet-mbn29/files/100805807.pdf" }, "resource_type": "article", "pub_year": "2012", "author_list": "Bruno, O. and Hoch, D." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/q0ny8-c8d64", "eprint_id": 28413, "eprint_status": "archive", "datestamp": "2023-08-22 03:54:06", "lastmod": "2023-10-24 17:52:39", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Shahbazi-K", "name": { "family": "Shahbazi", "given": "Khosro" } }, { "id": "Albin-N", "name": { "family": "Albin", "given": "Nathan" } }, { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar P." }, "orcid": "0000-0001-8369-3014" }, { "id": "Hesthaven-J-S", "name": { "family": "Hesthaven", "given": "Jan S." } } ] }, "title": "Multi-domain Fourier-continuation/WENO hybrid solver for conservation laws", "ispublished": "pub", "full_text_status": "restricted", "keywords": "Fourier continuation methods; High-order WENO methods; Multi-resolution methods; Conservation laws; Shock waves", "note": "\u00a9 2011 Elsevier Inc. Received 18 October 2010; revised 26 August 2011; Accepted 28 August 2011. Available online 7 September 2011. This work was financially supported by US Department of Energy, under Contract DE-FG02-98ER25346. N.A. and O.B. gratefully acknowledge support from AFOSR and NSF. The careful reading and excellent comments by reviewers are highly appreciated.", "abstract": "We introduce a multi-domain Fourier-continuation/WENO hybrid method (FC\u2013WENO) that enables high-order and non-oscillatory solution of systems of nonlinear conservation laws, and which enjoys essentially dispersionless, spectral character away from discontinuities, as well as mild CFL constraints (comparable to those of finite difference methods). The hybrid scheme employs the expensive, shock-capturing WENO method in small regions containing discontinuities and the efficient FC method in the rest of the computational domain, yielding a highly effective overall scheme for applications with a mix of discontinuities and complex smooth structures. The smooth and discontinuous solution regions are distinguished using the multi-resolution procedure of Harten [J. Comput. Phys. 115 (1994) 319\u2013338]. We consider WENO schemes of formal orders five and nine and a FC method of order five. The accuracy, stability and efficiency of the new hybrid method for conservation laws is investigated for problems with both smooth and non-smooth solutions. In the latter case, we solve the Euler equations for gas dynamics for the standard test case of a Mach three shock wave interacting with an entropy wave, as well as a shock wave (with Mach 1.25, three or six) interacting with a very small entropy wave and evaluate the efficiency of the hybrid FC\u2013WENO method as compared to a purely WENO-based approach as well as alternative hybrid based techniques. We demonstrate considerable computational advantages of the new FC-based method, suggesting a potential of an order of magnitude acceleration over alternatives when extended to fully three-dimensional problems.", "date": "2011-10-01", "date_type": "published", "publication": "Journal of Computational Physics", "volume": "230", "number": "24", "publisher": "Elsevier", "pagerange": "8779-8796", "id_number": "CaltechAUTHORS:20111212-085019337", "issn": "0021-9991", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20111212-085019337", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG02-98ER25346" }, { "agency": "Air Force Office of Scientific Research (AFOSR)" }, { "agency": "NSF" } ] }, "doi": "10.1016/j.jcp.2011.08.024", "resource_type": "article", "pub_year": "2011", "author_list": "Shahbazi, Khosro; Albin, Nathan; et el." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/mjfav-cga35", "eprint_id": 24513, "eprint_status": "archive", "datestamp": "2023-08-22 03:11:21", "lastmod": "2023-10-23 23:24:43", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Albin-N", "name": { "family": "Albin", "given": "Nathan" } }, { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar P." }, "orcid": "0000-0001-8369-3014" } ] }, "title": "A spectral FC solver for the compressible Navier\u2013Stokes equations in general domains I: Explicit time-stepping", "ispublished": "pub", "full_text_status": "restricted", "keywords": "Spectral method; Complex geometry; Fourier series; Fourier continuation; Partial differential equation; Compressible Navier-Stokes; Direct numerical simulation; Numerical dispersion", "note": "\u00a9 2011 Elsevier Inc. Received 9 November 2010; revised 16 April 2011; accepted 18 April 2011. Available online 28 April 2011. NA gratefully acknowledges the support of the NSF postdoctoral fellowship. NA and OB gratefully acknowledge support from NSF and AFOSR.", "abstract": "We present a Fourier continuation (FC) algorithm for the solution of the fully nonlinear compressible Navier\u2013Stokes equations in general spatial domains. The new scheme is based on the recently introduced accelerated FC method, which enables use of highly accurate Fourier expansions as the main building block of general-domain PDE solvers. Previous FC-based PDE solvers are restricted to linear scalar equations with constant coefficients. The FC methodology presented in this text thus constitutes a significant generalization of the previous FC schemes, as it yields general-domain FC solvers for nonlinear systems of PDEs. While not restricted to periodic boundary conditions and therefore applicable to general boundary value problems on arbitrary domains, the proposed algorithm inherits many of the highly desirable properties arising from rapidly convergent Fourier expansions, including high-order convergence, essentially spectrally accurate dispersion relations, and much milder CFL constraints than those imposed by polynomial-based spectral methods\u2014since, for example, the spectral radius of the FC first derivative grows linearly with the number of spatial discretization points. We demonstrate the accuracy and optimal parallel efficiency of the algorithm in a variety of scientific and engineering contexts relevant to fluid-dynamics and nonlinear acoustics.", "date": "2011-07-10", "date_type": "published", "publication": "Journal of Computational Physics", "volume": "230", "number": "16", "publisher": "Elsevier", "pagerange": "6248-6270", "id_number": "CaltechAUTHORS:20110725-065924210", "issn": "0021-9991", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20110725-065924210", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF Postdoctoral Fellowship" }, { "agency": "NSF" }, { "agency": "Air Force Office of Scientific Research (AFOSR)" } ] }, "doi": "10.1016/j.jcp.2011.04.023", "resource_type": "article", "pub_year": "2011", "author_list": "Albin, Nathan and Bruno, Oscar P." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/p24wv-j1920", "eprint_id": 22046, "eprint_status": "archive", "datestamp": "2023-08-22 02:07:27", "lastmod": "2023-10-23 15:38:19", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Nacev-A", "name": { "family": "Nacev", "given": "A." } }, { "id": "Beni-C", "name": { "family": "Beni", "given": "C." } }, { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "O." }, "orcid": "0000-0001-8369-3014" }, { "id": "Shapiro-B", "name": { "family": "Shapiro", "given": "B." } } ] }, "title": "The behaviors of ferromagnetic nano-particles in and around blood vessels under applied magnetic fields", "ispublished": "pub", "full_text_status": "restricted", "keywords": "Magnetic drug targeting; Ferromagnetic nanoparticles; Simulations; Tissue; Blood vessels; Treatment depth; Non-dimensional parameters; In-vivo experiments", "note": "\u00a9 2010 Elsevier B.V.\n\nReceived 11 March 2010; revised 26 August 2010. Available online 22 September 2010.\n\nThis research was supported in part by NIBIB/NIH grant number R21EB009265. We would like to thank the support provided by a NPSC graduate fellowship in addition to support from the Air Force Office of Scientific Research and the National Science Foundation.", "abstract": "In magnetic drug delivery, therapeutic magnetizable particles are typically injected into the blood stream and magnets are then used to concentrate them to disease locations. The behavior of such particles in-vivo is complex and is governed by blood convection, diffusion (in blood and in tissue), extravasation, and the applied magnetic fields. Using physical first-principles and a sophisticated vessel-membrane-tissue (VMT) numerical solver, we comprehensively analyze in detail the behavior of magnetic particles in blood vessels and surrounding tissue. For any blood vessel (of any size, depth, and blood velocity) and tissue properties, particle size and applied magnetic fields, we consider a Krogh tissue cylinder geometry and solve for the resulting spatial distribution of particles. We find that there are three prototypical behaviors (blood velocity dominated, magnetic force dominated, and boundary-layer formation) and that the type of behavior observed is uniquely determined by three non-dimensional numbers (the magnetic-Richardson number, mass P\u00e9clet number, and Renkin reduced diffusion coefficient). Plots and equations are provided to easily read out which behavior is found under which circumstances ([Fig. 5], [Fig. 6], [Fig. 7] and [Fig. 8]). We compare our results to previously published in-vitro and in-vivo magnetic drug delivery experiments. Not only do we find excellent agreement between our predictions and prior experimental observations, but we are also able to qualitatively and quantitatively explain behavior that was previously not understood.", "date": "2011-03", "date_type": "published", "publication": "Journal of Magnetism and Magnetic Materials", "volume": "323", "number": "6", "publisher": "Elsevier", "pagerange": "651-668", "id_number": "CaltechAUTHORS:20110207-101558443", "issn": "0304-8853", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20110207-101558443", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "National Institute of Biomedical Imaging and Bioengineering (NIBB)/NIH", "grant_number": "R21EB009265" }, { "agency": "National Physical Science Consortium (NPSC)" }, { "agency": "Air Force Office of Scientific Research (AFOSR)" }, { "agency": "NSF" } ] }, "doi": "10.1016/j.jmmm.2010.09.008", "resource_type": "article", "pub_year": "2011", "author_list": "Nacev, A.; Beni, C.; et el." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/jadfw-4sk51", "eprint_id": 21363, "eprint_status": "archive", "datestamp": "2023-08-19 04:14:27", "lastmod": "2023-10-20 23:58:35", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar P." }, "orcid": "0000-0001-8369-3014" }, { "id": "Haslam-M-C", "name": { "family": "Haslam", "given": "Michael C." } } ] }, "title": "Efficient high-order evaluation of scattering by periodic surfaces: vector-parametric gratings and geometric singularities", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 2010 Taylor & Francis.\nReceived 4 January 2010; final version received 26 May 2010.\nFirst Published on: 31 August 2010.\n\nOB gratefully acknowledges support by the Air Force Office of Scientific Research and the National Science Foundation. MH gratefully acknowledges the support of the Natural Sciences and Engineering Research Council of Canada.", "abstract": "We introduce a highly accurate and efficient solver for problems of scattering by vector-parametric, possibly non-smooth one-dimensional periodic surfaces. For grating-diffraction problems in the resonance regime (heights and periods of the order of the wavelength of radiation) the proposed algorithm produces solutions with full double-precision accuracy in single-processor computing times of the order of a few seconds. Our algorithm can also produce, in reasonable computing times, solutions for highly challenging TE and TM scattering problems - defined by very deep multi-valued scattering surfaces and high frequencies of radiation - including cases in which non-smooth bounding surfaces enclose open cavities.", "date": "2010-11", "date_type": "published", "publication": "Waves in Random and Complex Media", "volume": "20", "number": "4", "publisher": "Taylor & Francis", "pagerange": "530-550", "id_number": "CaltechAUTHORS:20101214-135627503", "issn": "1745-5030", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20101214-135627503", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Air Force Office of Scientific Research (AFOSR)" }, { "agency": "NSF" }, { "agency": "Natural Sciences and Engineering Research Council of Canada (NSERC)" } ] }, "doi": "10.1080/17455030.2010.499151", "resource_type": "article", "pub_year": "2010", "author_list": "Bruno, Oscar P. and Haslam, Michael C." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/qyjc7-w3r51", "eprint_id": 22159, "eprint_status": "archive", "datestamp": "2023-08-22 01:17:16", "lastmod": "2023-10-23 15:45:22", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Nacev-A", "name": { "family": "Nacev", "given": "A." } }, { "id": "Beni-C", "name": { "family": "Beni", "given": "C." } }, { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "O." }, "orcid": "0000-0001-8369-3014" }, { "id": "Shapiro-B", "name": { "family": "Shapiro", "given": "B." } } ] }, "title": "Magnetic nanoparticle transport within flowing blood and into surrounding tissue", "ispublished": "pub", "full_text_status": "public", "keywords": "blood vessels; ferromagnetic nanoparticles; in vivo experiments; magnetic drug targeting; nondimensional parameters; simulations; tissue treatment depth", "note": "\u00a9 2010 Future Medicine Ltd.\n\nThis research was supported in part by NIBIB/NIH grant\nnumber R21EB009265. We would like to thank the support\nprovided by a NPSC graduate fellowship in addition\nto support from the Air Force Office of Scientific Research\nand the National Science Foundation. The authors have\nno other relevant affiliations or financial involvement\nwith any organization or entity with a financial interest\nin or financial conflict with the subject matter or materials\ndiscussed in the manuscript apart from those disclosed.\nNo writing assistance was utilized in the production of\nthis manuscript.\n\nPublished - Nacev2010p12592Nanomedicine-Uk.pdf
Accepted Version - nihms-268991.pdf
", "abstract": "Magnetic drug delivery refers to the physical confinement of therapeutic magnetic nanoparticles to\nregions of disease, tumors, infections and blood clots. Predicting the effectiveness of magnetic focusing\nin vivo is critical for the design and use of magnetic drug delivery systems. However, current simple\nback-of-the-envelope estimates have proven insufficient for this task. In this article, we present an\nanalysis of nanoparticle distribution, in and around a single blood vessel (a Krogh tissue cylinder),\nlocated at any depth in the body, with any physiologically relevant blood flow velocity, diffusion and\nextravasation properties, and with any applied magnetic force on the particles. For any such blood\nvessel our analysis predicts one of three distinct types of particle behavior (velocity dominated,\nmagnetic dominated or boundary-layer formation), which can be uniquely determined by looking up\nthe values of three nondimensional numbers we define. We compare our predictions to previously\npublished magnetic-focusing in vitro and in vivo studies. Not only do we find agreement between our\npredictions and prior observations, but we are also able to quantitatively explain behavior that was\nnot understood previously.", "date": "2010-11", "date_type": "published", "publication": "Nanomedicine", "volume": "5", "number": "9", "publisher": "Future Medicine", "pagerange": "1459-1466", "id_number": "CaltechAUTHORS:20110214-092710313", "issn": "1743-5889", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20110214-092710313", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NIH", "grant_number": "R21EB009265" }, { "agency": "National Physical Science Consortium" }, { "agency": "Air Force Office of Scientific Research (AFOSR)" }, { "agency": "NSF" } ] }, "doi": "10.2217/NNM.10.104", "pmcid": "PMC3057021", "primary_object": { "basename": "nihms-268991.pdf", "url": "https://authors.library.caltech.edu/records/qyjc7-w3r51/files/nihms-268991.pdf" }, "related_objects": [ { "basename": "Nacev2010p12592Nanomedicine-Uk.pdf", "url": "https://authors.library.caltech.edu/records/qyjc7-w3r51/files/Nacev2010p12592Nanomedicine-Uk.pdf" } ], "resource_type": "article", "pub_year": "2010", "author_list": "Nacev, A.; Beni, C.; et el." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/3cpq4-zbz47", "eprint_id": 20501, "eprint_status": "archive", "datestamp": "2023-08-22 00:42:29", "lastmod": "2023-10-20 23:07:31", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "L\u00f3pez-V\u00e1zquez-J-C", "name": { "family": "L\u00f3pez-V\u00e1zquez", "given": "J. Carlos" } }, { "id": "De\u00e1n-Ben-X-L", "name": { "family": "De\u00e1n-Ben", "given": "X. Lu\u00eds" } }, { "id": "Trillo-C", "name": { "family": "Trillo", "given": "Cristina" } }, { "id": "Doval-A-F", "name": { "family": "Doval", "given": "\u00c1ngel F." } }, { "id": "Fern\u00e1ndez-J-L", "name": { "family": "Fern\u00e1ndez", "given": "Jos\u00e9 L." } }, { "id": "Amlani-F", "name": { "family": "Amlani", "given": "Faisal" } }, { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar P." }, "orcid": "0000-0001-8369-3014" } ] }, "title": "Numerical modeling and measurement by pulsed television holography of ultrasonic displacement maps in plates with through-thickness defects", "ispublished": "pub", "full_text_status": "public", "keywords": "pulsed television holography; nondestructive testing; ultrasonics; elastic waves; plates", "note": "\u00a9 2010 Society of Photo-Optical Instrumentation Engineers. \n\nPaper 100096PR received Feb. 4, 2010; revised manuscript received Jun. 21, 2010; accepted for publication Jul. 13, 2010; published online Sep. 30, 2010. \n\nThis work was cofunded by the Spanish Ministerio de Ciencia e Innovaci\u00f3n and by the European Comission ERDF in the context of the Plan Nacional de I+D+i project number DPI2008-02709, and by the Direcci\u00f3n Xeral de Investigaci\u00f3n, Desenvolvemento e Innovaci\u00f3n da Xunta de Galicia in the context of the Plan Galego de IDIT project number INCITE08PXIB303252PR. Supplementary cofunding from the Universidade de Vigo project number I608122F64102 is also acknowledged. Amlani and Bruno gratefully acknowledge support by the Air Force Office of Scientific Research and the National Science Foundation.\n\nPublished - CarlosLopezVazquez2010p11635Opt_Eng.pdf
", "abstract": "We present a novel numerical modeling of ultrasonic Lamb and Rayleigh wave propagation and scattering by through-thickness defects like holes and slots in homogeneous plates, and its experimental verification in both near and far field by a self-developed pulsed TV holography system. In contrast to rigorous vectorial formulation of elasticity theory, our model is based on the 2-D scalar wave equation over the plate surface, with specific boundary conditions in the defects and plate edges. The experimental data include complex amplitude maps of the out-of-plane displacements of the plate surface, obtained by a two-step spatiotemporal Fourier transform method. We find a fair match between the numerical and experimental results, which allows for quantitative characterization of the defects.", "date": "2010-09", "date_type": "published", "publication": "Optical Engineering", "volume": "49", "number": "9", "publisher": "Society of Photo-Optical Instrumentation Engineers", "pagerange": "Art. No. 095802", "id_number": "CaltechAUTHORS:20101025-104450688", "issn": "0091-3286", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20101025-104450688", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Ministerio de Ciencia e Innovaci\u00f3n (MCINN)" }, { "agency": "European Commission (ERDF)", "grant_number": "DPI2008-02709" }, { "agency": "Direccion Xeral de Investigacion, Desenvolvemento e Innovacion da Xunta de Galicia", "grant_number": "INCITE08PXIB303252PR" }, { "agency": "Universidade de Vigo", "grant_number": "I608122F64102" }, { "agency": "Air Force Office of Scientific Research (AFOSR)" }, { "agency": "NSF" } ] }, "doi": "10.1117/1.3484953", "primary_object": { "basename": "CarlosLopezVazquez2010p11635Opt_Eng.pdf", "url": "https://authors.library.caltech.edu/records/3cpq4-zbz47/files/CarlosLopezVazquez2010p11635Opt_Eng.pdf" }, "resource_type": "article", "pub_year": "2010", "author_list": "L\u00f3pez-V\u00e1zquez, J. Carlos; De\u00e1n-Ben, X. Lu\u00eds; et el." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/9r14n-m9a94", "eprint_id": 18367, "eprint_status": "archive", "datestamp": "2023-08-21 23:54:25", "lastmod": "2023-10-20 16:09:38", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Lyon-M", "name": { "family": "Lyon", "given": "Mark" } }, { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar P." }, "orcid": "0000-0001-8369-3014" } ] }, "title": "High-order unconditionally stable FC-AD solvers for general smooth domains II. Elliptic, parabolic and hyperbolic PDEs; theoretical considerations", "ispublished": "pub", "full_text_status": "restricted", "keywords": "Spectral method; Complex geometry; Unconditional stability; Fourier series; Fourier Continuation; ADI; Partial differential equation; Numerical method", "note": "\u00a9 2010 Elsevier Inc. \n\nReceived 17 April 2009; revised 1 January 2010; accepted 7 January 2010. Available online 20 January 2010. \n\nWe gratefully acknowledge support by the Air Force Office of Scientific Research and the National Science Foundation.", "abstract": "A new PDE solver was introduced recently, in Part I of this two-paper sequence, on the basis of two main concepts: the well-known Alternating Direction Implicit (ADI) approach, on one hand, and a certain \"Fourier Continuation\" (FC) method for the resolution of the Gibbs phenomenon, on the other. Unlike previous alternating direction methods of order higher than one, which only deliver unconditional stability for rectangular domains, the new high-order FC-AD (Fourier-Continuation Alternating-Direction) algorithm yields unconditional stability for general domains\u2014at an O(N log(N)) cost per time-step for an N point spatial discretization grid. In the present contribution we provide an overall theoretical discussion of the FC-AD approach and we extend the FC-AD methodology to linear hyperbolic PDEs. In particular, we study the convergence properties of the newly introduced FC(Gram) Fourier Continuation method for both approximation of general functions and solution of the alternating-direction ODEs. We also present (for parabolic PDEs on general domains, and, thus, for our associated elliptic solvers) a stability criterion which, when satisfied, ensures unconditional stability of the FC-AD algorithm. Use of this criterion in conjunction with numerical evaluation of a series of singular values (of the alternating-direction discrete one-dimensional operators) suggests clearly that the fifth-order accurate class of parabolic and elliptic FC-AD solvers we propose is indeed unconditionally stable for all smooth spatial domains and for arbitrarily fine discretizations. To illustrate the FC-AD methodology in the hyperbolic PDE context, finally, we present an example concerning the Wave Equation\u2014demonstrating sixth-order spatial and fourth-order temporal accuracy, as well as a complete absence of the debilitating \"dispersion error\", also known as \"pollution error\", that arises as finite-difference and finite-element solvers are applied to solution of wave propagation problems.", "date": "2010-05-01", "date_type": "published", "publication": "Journal of Computational Physics", "volume": "229", "number": "9", "publisher": "Elsevier", "pagerange": "3358-3381", "id_number": "CaltechAUTHORS:20100520-133258749", "issn": "0021-9991", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20100520-133258749", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Air Force Office of Scientific Research (AFOSR)" }, { "agency": "NSF" } ] }, "doi": "10.1016/j.jcp.2010.01.006", "resource_type": "article", "pub_year": "2010", "author_list": "Lyon, Mark and Bruno, Oscar P." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/pk0f3-emm19", "eprint_id": 17785, "eprint_status": "archive", "datestamp": "2023-08-21 23:36:35", "lastmod": "2023-10-20 00:13:45", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar P." }, "orcid": "0000-0001-8369-3014" }, { "id": "Lyon-M", "name": { "family": "Lyon", "given": "Mark" } } ] }, "title": "High-order unconditionally stable FC-AD solvers for general smooth domains I. Basic elements", "ispublished": "pub", "full_text_status": "restricted", "keywords": "Spectral method; Complex geometry; Unconditional stability; Fourier series; Fourier continuation; ADI; Partial Differential Equation; Numerical method", "note": "\u00a9 2009 Elsevier Inc. \n\nReceived 17 April 2009. Received in revised form 25 October 2009. Accepted 11 November 2009. Available online 18 November 2009. \n\nWe gratefully acknowledge support by the Air Force Office of Scientific Research and the National Science Foundation.", "abstract": "We introduce a new methodology for the numerical solution of Partial Differential Equations\nin general spatial domains: our algorithms are based on the use of the well-known\nAlternating Direction Implicit (ADI) approach in conjunction with a certain \"Fourier continuation\"\n(FC) method for the resolution of the Gibbs phenomenon. Unlike previous alternating\ndirection methods of order higher than one, which can only deliver unconditional\nstability for rectangular domains, the present high-order algorithms possess the desirable\nproperty of unconditional stability for general domains; the computational time required by\nour algorithms to advance a solution by one time-step, in turn, grows in an essentially linear\nmanner with the number of spatial discretization points used. In this paper we demonstrate\nthe FC-AD methodology through a variety of examples concerning the Heat and\nLaplace Equations in two and three-dimensional domains with smooth boundaries. Applications\nof the FC-AD methodology to Hyperbolic PDEs together with a theoretical discussion\nof the method will be put forth in a subsequent contribution. The numerical\nexamples presented in this text demonstrate the unconditional stability and high-order\nconvergence of the proposed algorithms, as well the very significant improvements they\ncan provide (in one of our examples we demonstrate a one thousand improvement factor)\nover the computing times required by some of the most efficient alternative general-domain\nsolvers.", "date": "2010-03-20", "date_type": "published", "publication": "Journal of Computational Physics", "volume": "229", "number": "6", "publisher": "Elsevier", "pagerange": "2009-2033", "id_number": "CaltechAUTHORS:20100324-103102353", "issn": "0021-9991", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20100324-103102353", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Air Force Office of Scientific Research (AFOSR)" }, { "agency": "NSF" } ] }, "doi": "10.1016/j.jcp.2009.11.020", "resource_type": "article", "pub_year": "2010", "author_list": "Bruno, Oscar P. and Lyon, Mark" }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/445m6-16g12", "eprint_id": 15326, "eprint_status": "archive", "datestamp": "2023-08-21 22:21:50", "lastmod": "2023-10-18 21:40:25", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar" }, "orcid": "0000-0001-8369-3014" }, { "id": "Elling-T", "name": { "family": "Elling", "given": "Tim" } }, { "id": "Paffenroth-R-C", "name": { "family": "Paffenroth", "given": "Randy" } }, { "id": "Turc-C", "name": { "family": "Turc", "given": "Catalin" } } ] }, "title": "Electromagnetic integral equations requiring small numbers of Krylov-subspace iterations", "ispublished": "pub", "full_text_status": "restricted", "keywords": "Electromagnetic scattering; Combined Field Integral Equations; Pseudodifferential operators; Regularizing operator", "note": "\u00a9 2009 Elsevier. \n\nReceived 21 October 2008; revised 23 April 2009; accepted 11 May 2009. Available online 20 May 2009. \n\nWe gratefully acknowledge support by the Air Force Office of Scientific Research and the National Science Foundation.", "abstract": "We present a new class of integral equations for the solution of problems of scattering of electromagnetic fields by perfectly conducting bodies. Like the classical Combined Field Integral Equation (CFIE), our formulation results from a representation of the scattered field as a combination of magnetic- and electric-dipole distributions on the surface of the scatterer. In contrast with the classical equations, however, the electric-dipole operator we use contains a regularizing operator; we call the resulting equations Regularized Combined Field Integral Equations (CFIE-R). Unlike the CFIE, the CFIE-R are Fredholm equations which, we show, are uniquely solvable; our selection of coupling parameters, further, yields CFIE-R operators with excellent spectral distributions\u2014with closely clustered eigenvalues\u2014so that small numbers of iterations suffice to solve the corresponding equations by means of Krylov subspace iterative solvers such as GMRES. The regularizing operators are constructed on the basis of the single layer operator, and can thus be incorporated easily within any existing surface integral equation implementation for the solution of the classical CFIE. We present one such methodology: a high-order Nystr\u00f6m approach based on use of partitions of unity and trapezoidal-rule integration. A variety of numerical results demonstrate very significant gains in computational costs that can result from the new formulations, for a given accuracy, over those arising from previous approaches.", "date": "2009-09-20", "date_type": "published", "publication": "Journal of Computational Physics", "volume": "228", "number": "17", "publisher": "Elsevier", "pagerange": "6169-6183", "id_number": "CaltechAUTHORS:20090826-112852554", "issn": "0021-9991", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20090826-112852554", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Air Force Office of Scientific Research (AFOSR)" }, { "agency": "NSF" } ] }, "doi": "10.1016/j.jcp.2009.05.020", "resource_type": "article", "pub_year": "2009", "author_list": "Bruno, Oscar; Elling, Tim; et el." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/pzf2k-tjg25", "eprint_id": 73690, "eprint_status": "archive", "datestamp": "2023-08-20 02:05:06", "lastmod": "2024-01-13 20:24:02", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "L\u00f3pez-V\u00e1zquez-J-C", "name": { "family": "L\u00f3pez-V\u00e1zquez", "given": "J. Carlos" } }, { "id": "De\u00e1n-J-L", "name": { "family": "De\u00e1n", "given": "J. Luis" } }, { "id": "Trillo-C", "name": { "family": "Trillo", "given": "Cristina" } }, { "id": "Doval-A-F", "name": { "family": "Doval", "given": "\u00c1ngel F." } }, { "id": "Fern\u00e1ndez-J-L", "name": { "family": "Fern\u00e1ndez", "given": "Jos\u00e9 L." } }, { "id": "Amlani-F", "name": { "family": "Amlani", "given": "Faisal" } }, { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar P." }, "orcid": "0000-0001-8369-3014" } ] }, "title": "Modelling for characterizing defects in plates using two-dimensional maps of instantaneous ultrasonic out-of-plane displacement obtained by pulsed TV-holography", "ispublished": "unpub", "full_text_status": "public", "keywords": "Pulsed TV holography, ESPI, Guided waves, Elastic scattering", "note": "\u00a9 2009 International Society for Optical Engineering SPIE. \n\nThis work was co-funded by the Spanish Ministerio de Ciencia e Innovaci\u03ccn and by the European Comission (ERDF) in the context of the Plan Nacional de I+D+i (project number DPI2008-02709) and by the Direcci\u03ccn Xeral de Investigaci\u03ccn, Desenvolvemento e Innovaci\u03ccn da Xunta de Galicia in the context of the Plan Galego de IDIT (project number INCITE08PXIB303252PR). Supplementary co-funding from the Universidade de Vigo (project number I608122F64102) is also acknowledged. Faisal Amlani and Oscar Bruno gratefully acknowledge support by the Air Force Office of Scientific Research and the National Science Foundation.\n\nPublished - 738937_1.pdf
", "abstract": "It has been demonstrated that non-destructive inspection of plates can be performed by using two-dimensional maps of instantaneous out-of-plane displacements obtained with a self-developed pulsed TV-holography system. Specifically, the interaction of guided elastic waves with defects produces scattering patterns that contain information about the defects (position, dimensions, orientation, etc.). For quantitative characterization on this basis, modeling of the wave propagation and interaction with the defects is necessary. In fact, the development of models for scattering of waves in plates is yet an active research field in which the most reliable approach is usually based on the rigorous formulation of elasticity theory. By contrast, in this work the capability of a simple two-dimensional scalar model for obtaining a quantitative description of the output two-dimensional maps associated to artificial defects in plates is studied. Some experiments recording the interaction of narrowband Rayleigh waves with artificial defects in aluminum plates are presented, in which the acoustic field is obtained from the TV-holography optical phase-change maps by means of a specially developed two-step spatio-temporal Fourier transform method. For the modeling, harmonic regime and free-stress boundary conditions are assumed. Comparisons between experimental and simulated maps are included for defects with different shapes.", "date": "2009-06-15", "date_type": "published", "publisher": "Society of Photo-Optical Instrumentation Engineers (SPIE)", "place_of_pub": "Bellingham, WA", "pagerange": "Art. No. 738937", "id_number": "CaltechAUTHORS:20170125-073103435", "isbn": "9780819476722", "book_title": "Optical Measurement Systems for Industrial Inspection VI", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170125-073103435", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Ministerio de Ciencia e Innovaci\u03ccn (MICINN)" }, { "agency": "European Commission (ERDF)", "grant_number": "DPI2008-02709" }, { "agency": "Direccion Xeral de Investigaci\u03ccn, Desenvolvemento e Innovaci\u03ccn da Xunta de Galicia", "grant_number": "INCITE08PXIB303252PR" }, { "agency": "Universidade de Vigo", "grant_number": "I608122F64102" }, { "agency": "Air Force Office of Scientific Research (AFOSR)" }, { "agency": "NSF" } ] }, "contributors": { "items": [ { "id": "Lehmann-P-H", "name": { "family": "Lehmann", "given": "Peter H." } } ] }, "doi": "10.1117/12.827819", "primary_object": { "basename": "738937_1.pdf", "url": "https://authors.library.caltech.edu/records/pzf2k-tjg25/files/738937_1.pdf" }, "resource_type": "book_section", "pub_year": "2009", "author_list": "L\u00f3pez-V\u00e1zquez, J. Carlos; De\u00e1n, J. Luis; et el." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/vxqhs-36760", "eprint_id": 14636, "eprint_status": "archive", "datestamp": "2023-08-21 21:30:53", "lastmod": "2023-10-18 18:09:56", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar P." }, "orcid": "0000-0001-8369-3014" }, { "id": "Ovall-J-S", "name": { "family": "Ovall", "given": "Jeffrey S." } }, { "id": "Turc-C", "name": { "family": "Turc", "given": "Catalin" } } ] }, "title": "A high-order integral algorithm for highly singular PDE solutions in Lipschitz domains", "ispublished": "pub", "full_text_status": "restricted", "keywords": "Boundary value problems; Second-kind integral equations; Singular solution; High-order methods", "note": "\u00a9 2009 Springer. \n\nReceived: 4 November 2008; accepted: 6 April 2009; published online: 24 April 2009.", "abstract": "We present a new algorithm, based on integral equation formulations, for the solution of constant-coefficient elliptic partial differential equations (PDE) in closed two-dimensional domains with non-smooth boundaries; we focus on cases in which the integral-equation solutions as well as physically meaningful quantities (such as, stresses, electric/magnetic fields, etc.) tend to infinity at singular boundary points (corners). While, for simplicity, we restrict our discussion to integral equations associated with the Neumann problem for the Laplace equation, the proposed methodology applies to integral equations arising from other types of PDEs, including the Helmholtz, Maxwell, and linear elasticity equations. Our numerical results demonstrate excellent convergence as discretizations are refined, even around singular points at which solutions tend to infinity. We demonstrate the efficacy of this algorithm through applications to solution of Neumann problems for the Laplace operator over a variety of domains\u2014including domains containing extremely sharp concave and convex corners, with angles as small as \u03c0/100 and as large as 199\u03c0/100.", "date": "2009-06", "date_type": "published", "publication": "Computing", "volume": "84", "number": "3-4", "publisher": "Springer", "pagerange": "149-181", "id_number": "CaltechAUTHORS:20090722-113431556", "issn": "1436-5057", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20090722-113431556", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "doi": "10.1007/s00607-009-0031-1", "resource_type": "article", "pub_year": "2009", "author_list": "Bruno, Oscar P.; Ovall, Jeffrey S.; et el." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/v7cxb-x5n49", "eprint_id": 13948, "eprint_status": "archive", "datestamp": "2023-08-20 01:01:24", "lastmod": "2023-10-18 15:59:08", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Chaubell-J", "name": { "family": "Chaubell", "given": "Julian" } }, { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar P." }, "orcid": "0000-0001-8369-3014" }, { "id": "Ao-C-O", "name": { "family": "Ao", "given": "Chi O." } } ] }, "title": "Evaluation of EM-wave propagation in fully three-dimensional atmospheric refractive index distributions", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2009 American Geophysical Union.\nReceived 25 April 2008; revised 7 October 2008; accepted 18 December 2008; published 28 February 2009.\nThis work was supported in part\nby the Air Force Office of Scientific Research, the National\nScience Foundation and the National Aeronautics and Space\nAdministration. This research was performed, in part, while\nJulian Chaubell held a National Research Council Research\nAssociateship Award at Jet Propulsion Laboratory.\n\nPublished - Chaubell2009p53810.10292008RS003882.pdf
", "abstract": "We present a novel numerical method, based on high-frequency localization, for evaluation of electromagnetic-wave propagation through atmospheres exhibiting fully three-dimensional (height, range and cross-range) refractive index variations. This methodology, which is based on localization of Rytov-integration domains to small tubes around geometrical optics paths, can accurately solve three-dimensional propagation problems in orders-of-magnitude shorter computing times than other algorithms available presently. For example, the proposed approach can accurately produce solutions for propagation of \u224820 cm GPS signals across hundreds of kilometers of realistic, three-dimensional atmospheres in computing times on the order of 1 hour in a present-day single-processor workstation, a task for which other algorithms would require, in such single-processor computers, computing times on the order of several months.", "date": "2009-02-28", "date_type": "published", "publication": "Radio Science", "volume": "44", "publisher": "American Geophysical Union", "pagerange": "RS1012", "id_number": "CaltechAUTHORS:20090413-104957438", "issn": "0048-6604", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20090413-104957438", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Air Force Office of Scientific Research" }, { "agency": "NSF" }, { "agency": "NASA" }, { "agency": "Julian Chaubell held a National Research Council Research Associateship" }, { "agency": "JPL" } ] }, "doi": "10.1029/2008RS003882", "primary_object": { "basename": "Chaubell2009p53810.10292008RS003882.pdf", "url": "https://authors.library.caltech.edu/records/v7cxb-x5n49/files/Chaubell2009p53810.10292008RS003882.pdf" }, "resource_type": "article", "pub_year": "2009", "author_list": "Chaubell, Julian; Bruno, Oscar P.; et el." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/mqb8z-05e40", "eprint_id": 14973, "eprint_status": "archive", "datestamp": "2023-08-20 01:00:31", "lastmod": "2023-10-18 20:25:07", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar P." }, "orcid": "0000-0001-8369-3014" }, { "id": "Haslam-M-C", "name": { "family": "Haslam", "given": "Michael C." } } ] }, "title": "Efficient high-order evaluation of scattering by periodic surfaces: deep gratings, high frequencies, and glancing incidences", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2009 Optical Society of America. Received October 30, 2008; accepted December 10, 2008;\nposted December 22, 2008. (Doc. ID 103378); published February 25, 2009. O. P. Bruno gratefully acknowledges support by the U.S.\nAir Force Office of Scientific Research (AFOSR) and the\nNational Science Foundation (NSF). M. Haslam gratefully\nacknowledges the support of the Natural Sciences\nand Engineering Research Council of Canada. OCIS codes: 050.1755, 050.5745.\n\nPublished - Bruno2009p5486J._Opt._Soc._Amer._A.pdf
", "abstract": "We present a superalgebraically convergent integral equation algorithm for evaluation of TE and TM electromagnetic\nscattering by smooth perfectly conducting periodic surfaces z=f(x). For grating-diffraction problems\nin the resonance regime (heights and periods up to a few wavelengths) the proposed algorithm produces solutions\nwith full double-precision accuracy in single-processor computing times of the order of a few seconds. The\nalgorithm can also produce, in reasonable computing times, highly accurate solutions for very challenging\nproblems, such as (a) a problem of diffraction by a grating for which the peak-to-trough distance equals 40\ntimes its period that, in turn, equals 20 times the wavelength; and (b) a high-frequency problem with very\nsmall incidence, up to 0.01\u00b0 from glancing. The algorithm is based on the concurrent use of Floquet and Chebyshev\nexpansions together with certain integration weights that are computed accurately by means of an\nasymptotic expansion as the number of integration points tends to infinity.", "date": "2009-02-25", "date_type": "published", "publication": "Journal of the Optical Society of America A", "volume": "26", "number": "3", "publisher": "Optical Society of America", "pagerange": "658-668", "id_number": "CaltechAUTHORS:20090811-153042013", "issn": "1084-7529", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20090811-153042013", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Air Force Office of Scientific Research" }, { "agency": "NSF" }, { "agency": "Natural Sciences and Engineering Research Council of Canada" } ] }, "doi": "10.1364/JOSAA.26.000658", "primary_object": { "basename": "Bruno2009p5486J._Opt._Soc._Amer._A.pdf", "url": "https://authors.library.caltech.edu/records/mqb8z-05e40/files/Bruno2009p5486J._Opt._Soc._Amer._A.pdf" }, "resource_type": "article", "pub_year": "2009", "author_list": "Bruno, Oscar P. and Haslam, Michael C." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/hk4ak-fr055", "eprint_id": 14620, "eprint_status": "archive", "datestamp": "2023-08-19 23:57:29", "lastmod": "2023-10-18 18:09:07", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Berlyand-L", "name": { "family": "Berlyand", "given": "Leonid" } }, { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar" }, "orcid": "0000-0001-8369-3014" }, { "id": "Novikov-A", "name": { "family": "Novikov", "given": "Alexei" } } ] }, "title": "Rise of correlations of transformation strains in random polycrystals", "ispublished": "pub", "full_text_status": "public", "keywords": "polycrystals, misfit, phase transitions, correlations, De Finetti's theorem, Riesz' rearrangement inequality", "note": "\u00a9 2008 Society for Industrial and Applied Mathematics. Received by the editors January 9, 2007; accepted for publication (in revised form) June 24. 2008; published electronically November 19, 2008. We thank Alexei Borodin and Omri Sarig for useful discussions.\nWe are grateful to anonymous referees for their useful suggestions. AMS subject classifications. 35J20, 74N15, 82B44\n\nPublished - Berlyand2008p247Siam_J_Math_Anal.pdf
", "abstract": "We investigate the statistics of the transformation strains that arise in random martensitic polycrystals as boundary conditions cause its component crystallites to undergo martensitic phase transitions. In our laminated polycrystal model the orientation of the n grains (crystallites)\nis given by an uncorrelated random array of the orientation angles \u03b8_i, i = 1, . . . ,n. Under imposed boundary conditions the polycrystal grains may undergo a martensitic transformation. The associated transformation strains \u03b5_i, i = 1, . . . ,n depend on the array of orientation angles, and they can be obtained as a solution to a nonlinear optimization problem. While the random variables \u03b8_i,\ni = 1, . . . ,n are uncorrelated, the random variables \u03b5_i, i = 1, . . . ,n may be correlated. This issue is\ncentral in our considerations. We investigate it in following three different scaling limits: (i) Infinitely\nlong grains (laminated polycrystal of height L = \u221e); (ii) Grains of finite but large height (L \u00bb 1); and (iii) Chain of short grains (L = l_0/(2n), l_0 \u00ab 1). With references to de Finetti's theorem, Riesz'\nrearrangement inequality, and near neighbor approximations, our analyses establish that under the\nscaling limits (i), (ii), and (iii) the arrays of transformation strains arising from given boundary\nconditions exhibit no correlations, long-range correlations, and exponentially decaying short-range\ncorrelations, respectively", "date": "2008-11-19", "date_type": "published", "publication": "SIAM Journal on mathematical analysis", "volume": "40", "number": "4", "publisher": "SIAM Publications", "pagerange": "1550-1584", "id_number": "CaltechAUTHORS:20090720-151441316", "issn": "0036-1410", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20090720-151441316", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "doi": "10.1137/070679685", "primary_object": { "basename": "Berlyand2008p247Siam_J_Math_Anal.pdf", "url": "https://authors.library.caltech.edu/records/hk4ak-fr055/files/Berlyand2008p247Siam_J_Math_Anal.pdf" }, "resource_type": "article", "pub_year": "2008", "author_list": "Berlyand, Leonid; Bruno, Oscar; et el." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/hen2b-amf58", "eprint_id": 90651, "eprint_status": "archive", "datestamp": "2023-08-22 10:50:41", "lastmod": "2024-01-14 21:09:00", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "O. P." }, "orcid": "0000-0001-8369-3014" }, { "id": "Reitich-F", "name": { "family": "Reitich", "given": "F." } } ] }, "title": "High-Order Methods for High-Frequency Scattering Applications", "ispublished": "unpub", "full_text_status": "restricted", "keywords": "Circular Cylinder; Target Point; Boundary Integral Equation; Geometrical Optic; Eikonal Equation", "note": "\u00a9 2008 Springer-Verlag Berlin Heidelberg.", "abstract": "The problem of simulating the scattering of (acoustic, electromagnetic, elastic) waves has provided a particularly sustained, demanding and motivating challenge for the development of efficient and accurate numerical methods since the advent of computers. The classical issues present in most other applications, such as those related to the environmental and/or geometrical intricacies of the media in which quantities of interest are defined, are augmented in the context of wave propagation by the intrinsic complexities (i.e. oscillations) of the quantities themselves. Still, very efficient methodologies have been devised, particularly in the last twenty years, to simulate wave processes in rather complex settings. These techniques can be based, for instance, on finite elements (see e.g. [34, 35, 46] and the references therein), finite differences [40, 49] or boundary integral equations [4, 8, 11, 16, 25], and they can, today, effectively address these problems, with a high degree of accuracy, in domains that can span tens or perhaps even a few hundred wavelengths. The very nature of these classical approaches, however, limits their applicability at higher frequencies since the numerical resolution of field oscillations translates in a commensurately higher number of degrees of freedom and this, in turn, can easily lead to impractical computational times. In this chapter we review some recently proposed methodologies [5, 13\u201315, 29] that can overcome these limitations while retaining the mathematical rigor of classical numerical procedures.", "date": "2008", "date_type": "published", "publisher": "Springer", "place_of_pub": "Berlin", "pagerange": "129-163", "id_number": "CaltechAUTHORS:20181105-150853442", "isbn": "978-3-540-73777-3", "book_title": "Modeling and Computations in Electromagnetics: A Volume Dedicated to Jean-Claude N\u00e9d\u00e9lec", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20181105-150853442", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "contributors": { "items": [ { "id": "Ammari-H", "name": { "family": "Ammari", "given": "Habib" } } ] }, "doi": "10.1007/978-3-540-73778-0_5", "resource_type": "book_section", "pub_year": "2008", "author_list": "Bruno, O. P. and Reitich, F." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/d6et6-p5485", "eprint_id": 9423, "eprint_status": "archive", "datestamp": "2023-08-22 10:43:27", "lastmod": "2023-10-16 22:12:21", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar P." }, "orcid": "0000-0001-8369-3014" }, { "id": "Lintner-S", "name": { "family": "Lintner", "given": "St\u00e9phane" } } ] }, "title": "Superlens-cloaking of small dielectric bodies in the quasistatic regime", "ispublished": "pub", "full_text_status": "public", "keywords": "dielectric materials", "note": "\u00a92007 American Institute of Physics. \n\nReceived 24 August 2007; accepted 22 October 2007; published 26 December 2007. \n\nThe authors gratefully acknowledge support from USAFOSR (FA9550-05-1-0006) and NSF (DMS-0408040).", "abstract": "It has been conjectured that, in the quasistatic regime, dielectric bodies of finite size could be perfectly cloaked by certain cylindrical arrangements of materials of positive and negative permittivities known as superlenses. We show that, although they do not cloak perfectly dielectrics objects of any size, cylindrical superlenses do cloak, to a significant extent, dielectric bodies of small size.", "date": "2007-12-15", "date_type": "published", "publication": "Journal of Applied Physics", "volume": "102", "number": "12", "publisher": "Journal of Applied Physics", "pagerange": "Art. No. 124502", "id_number": "CaltechAUTHORS:BRUjap07", "issn": "0021-8979", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:BRUjap07", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "doi": "10.1063/1.2821759", "primary_object": { "basename": "BRUjap07.pdf", "url": "https://authors.library.caltech.edu/records/d6et6-p5485/files/BRUjap07.pdf" }, "resource_type": "article", "pub_year": "2007", "author_list": "Bruno, Oscar P. and Lintner, St\u00e9phane" }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/skdms-djd20", "eprint_id": 90587, "eprint_status": "archive", "datestamp": "2023-08-22 10:41:55", "lastmod": "2023-10-19 14:36:35", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar P." }, "orcid": "0000-0001-8369-3014" }, { "id": "Han-Youngae", "name": { "family": "Han", "given": "Youngae" } }, { "id": "Pohlman-M-M", "name": { "family": "Pohlman", "given": "Matthew M." } } ] }, "title": "Accurate, high-order representation of complex three-dimensional surfaces via Fourier continuation analysis", "ispublished": "pub", "full_text_status": "restricted", "keywords": "Continuation method; Surface representation; Fourier series; Edge matching; Parametrization by projection", "note": "\u00a9 2007 Elsevier. \n\nReceived 11 December 2006, Revised 24 August 2007, Accepted 28 August 2007, Available online 12 September 2007. \n\nThis work was supported in part by the Air Force Office of Scientific Research, the National Science Foundation and the National Aeronautics and Space Administration.", "abstract": "We present a new method for construction of high-order parametrizations of surfaces: starting from point clouds, the method we propose can be used to produce full surface parametrizations (by sets of local charts, each one representing a large surface patch \u2013 which, typically, contains thousands of the points in the original point-cloud) for complex surfaces of scientific and engineering relevance. The proposed approach accurately renders both smooth and non-smooth portions of a surface: it yields super-algebraically convergent Fourier series approximations to a given surface up to and including all points of geometric singularity, such as corners, edges, conical points, etc. In view of their C^\u221e smoothness (except at true geometric singularities) and their properties of high-order approximation, the surfaces produced by this method are suitable for use in conjunction with high-order numerical methods for boundary value problems in domains with complex boundaries, including PDE solvers, integral equation solvers, etc. Our approach is based on a very simple concept: use of Fourier analysis to continue smooth portions of a piecewise smooth function into new functions which, defined on larger domains, are both smooth and periodic. The \"continuation functions\" arising from a function f converge super-algebraically to f in its domain of definition as discretizations are refined. We demonstrate the capabilities of the proposed approach for a number of surfaces of engineering relevance.", "date": "2007-12-10", "date_type": "published", "publication": "Journal of Computational Physics", "volume": "227", "number": "2", "publisher": "Elsevier", "pagerange": "1094-1125", "id_number": "CaltechAUTHORS:20181101-152903783", "issn": "0021-9991", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20181101-152903783", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Air Force Office of Scientific Research (AFOSR)" }, { "agency": "NSF" }, { "agency": "NASA" } ] }, "doi": "10.1016/j.jcp.2007.08.029", "resource_type": "article", "pub_year": "2007", "author_list": "Bruno, Oscar P.; Han, Youngae; et el." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/gnb7a-36n36", "eprint_id": 8885, "eprint_status": "archive", "datestamp": "2023-08-22 10:01:19", "lastmod": "2023-10-16 21:47:36", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Weatherwax-J", "name": { "family": "Weatherwax", "given": "John" } }, { "id": "Vaynblat-D", "name": { "family": "Vaynblat", "given": "Dimitri" } }, { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar" }, "orcid": "0000-0001-8369-3014" }, { "id": "Rosales-R", "name": { "family": "Rosales", "given": "Ruben" } } ] }, "title": "On a viscous critical-stress model of martensitic phase transitions", "ispublished": "pub", "full_text_status": "public", "keywords": "critical phenomena; martensitic transformations; shock wave effects", "note": "\u00a92007 American Institute of Physics. \n\n(Received 26 February 2007; accepted 21 July 2007; published online 19 September 2007)", "abstract": "The solid-to-solid phase transitions that result from shock loading of certain materials, such as the graphite-to-diamond transition and the alpha-epsilon transition in iron, have long been subjects of a substantial theoretical and experimental literature. Recently a model for such transitions was introduced which, based on a CS condition (CS) and without use of fitting parameters, accounts quantitatively for existing observations in a number of systems [Bruno and Vaynblat, Proc. R. Soc. London, Ser. A 457, 2871 (2001)]. While the results of the CS model match the main features of the available experimental data, disagreements in some details between the predictions of this model and experiment, attributable to an ideal character of the CS model, do exist. In this article we present a version of the CS model, the viscous CS model (vCS), as well as a numerical method for its solution. This model and the corresponding solver results in a much improved overall CS modeling capability. The innovations we introduce include: (1) Enhancement of the model by inclusion of viscous phase-transition effects; as well as a numerical solver that allows for a fully rigorous treatment of both, the (2) Rarefaction fans (which had previously been approximated by \"rarefaction discontinuities\"), and (3) viscous phase-transition effects, that are part of the vCS model. In particular we show that the vCS model accounts accurately for well known \"gradual\" rises in the alpha-epsilon transition which, in the original CS model, were somewhat crudely approximated as jump discontinuities.", "date": "2007-09-15", "date_type": "published", "publication": "Journal of Applied Physics", "volume": "102", "number": "6", "publisher": "Journal of Applied Physics", "pagerange": "Art. No. 064905", "id_number": "CaltechAUTHORS:WEAjap07", "issn": "0021-8979", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:WEAjap07", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "doi": "10.1063/1.2778634", "primary_object": { "basename": "WEAjap07.pdf", "url": "https://authors.library.caltech.edu/records/gnb7a-36n36/files/WEAjap07.pdf" }, "resource_type": "article", "pub_year": "2007", "author_list": "Weatherwax, John; Vaynblat, Dimitri; et el." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/fdfhh-7wt85", "eprint_id": 19545, "eprint_status": "archive", "datestamp": "2023-08-22 09:31:36", "lastmod": "2023-10-20 20:48:14", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar P." }, "orcid": "0000-0001-8369-3014" }, { "id": "Geuzaine-C-A", "name": { "family": "Geuzaine", "given": "Christophe A." } } ] }, "title": "An O(1) integration scheme for three-dimensional surface scattering problems", "ispublished": "pub", "full_text_status": "restricted", "keywords": "wave scattering; boundary integral equations; high frequency methods", "note": "\u00a9 2006 Elsevier B.V. \n\nReceived 16 October 2005; received in revised form 7 February 2006.\nAvailable online 10 July 2006.", "abstract": "We present an accurate method of O(1)-complexity with respect to frequency (i.e., a method that, to achieve a prescribed error tolerance, requires a bounded computational cost for arbitrarily high frequencies) for the computation of singular oscillatory integrals arising in the boundary integral formulation of problems of acoustic scattering by surfaces in three-dimensional space. Like the two-dimensional counterpart of this algorithm, which we introduced recently and which is applicable to scattering by curves in the plane, the present method is based on a combination of two main elements: (1) a high-frequency ansatz for the unknown density in a boundary integral formulation of the problem, and (2) an extension of the ideas of the method of stationary phase to allow for O(1) (high-order-accurate) integration of oscillatory functions. The techniques we introduce to implement an efficient O(1) integrator in the present three-dimensional context differ significantly from those used in the earlier two-dimensional algorithm. In particular, in the present text, we introduce an efficient \"canonical\" (hybrid analytic-numerical) algorithm which, in addition to allowing for integration of oscillatory functions around both singular points and points of stationary phase, can handle the significant difficulty that arises as singular points and one or more stationary points approach each other within the two-dimensional scattering surface. We include numerical results illustrating the behavior of the integration algorithm on sound-soft spheres with diameters of up to 5000 wavelengths: in such cases, for a single integral, the algorithm yields accuracies of the order of three digits in computational times of less than two seconds. In a preliminary full scattering simulation we present, a solution with two digits of accuracy in the surface density was obtained in about three hours running time, in a single 1.5 GHz AMD Athlon processor, for a sphere of 500 wavelengths in diameter.", "date": "2007-07-15", "date_type": "published", "publication": "Journal of Computational and Applied Mathematics", "volume": "204", "number": "2", "publisher": "Elsevier", "pagerange": "463-476", "id_number": "CaltechAUTHORS:20100820-091539194", "issn": "0377-0427", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20100820-091539194", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "doi": "10.1016/j.cam.2006.02.050", "resource_type": "article", "pub_year": "2007", "author_list": "Bruno, Oscar P. and Geuzaine, Christophe A." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/nygc5-wbj85", "eprint_id": 9149, "eprint_status": "archive", "datestamp": "2023-08-22 09:18:54", "lastmod": "2023-10-16 21:56:25", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar P." }, "orcid": "0000-0001-8369-3014" }, { "id": "Haslam-M-C", "name": { "family": "Haslam", "given": "Michael C." } } ] }, "title": "Regularity Theory and Superalgebraic Solvers for Wire Antenna Problems", "ispublished": "pub", "full_text_status": "public", "keywords": "electromagnetic scattering; wire antenna; Pocklington; Hall\u00e9n", "note": "\u00a92007 Society for Industrial and Applied Mathematics. \n\nReceived by the editors December 22, 2005; accepted for publication (in revised form) December 27, 2006; published electronically June 12, 2007. This work was supported in part by the Air Force Office of Scientific Research, the National Science Foundation, and the National Aeronautics and Space Administration. \n\nThe second author [M.C.H.] was supported by the Natural Sciences and Engineering Research Council of Canada.", "abstract": "We consider the problem of evaluating the current distribution $J(z)$ that is induced on a straight wire antenna by a time-harmonic incident electromagnetic field. The scope of this paper is twofold. One of its main contributions is a regularity proof for a straight wire occupying the interval $[-1,1]$. In particular, for a smooth time-harmonic incident field this theorem implies that $J(z) = I(z)/\\sqrt{1-z^2}$, where $I(z)$ is an infinitely differentiable function\u2014the previous state of the art in this regard placed $I$ in the Sobolev space $W^{1,p}$, $p>1$. The second focus of this work is on numerics: we present three superalgebraically convergent algorithms for the solution of wire problems, two based on Hall\u00e9n's integral equation and one based on the Pocklington integrodifferential equation. Both our proof and our algorithms are based on two main elements: (1) a new decomposition of the kernel of the form $G(z) = F_1(z) \\ln\\! |z| + F_2(z)$, where $F_1(z)$ and $F_2(z)$ are analytic functions on the real line; and (2) removal of the end-point square root singularities by means of a coordinate transformation. The Hall\u00e9n- and Pocklington-based algorithms we propose converge superalgebraically: faster than $\\mathcal{O}(N^{-m})$ and $\\mathcal{O}(M^{-m})$ for any positive integer $m$, where $N$ and $M$ are the numbers of unknowns and the number of integration points required for construction of the discretized operator, respectively. In previous studies, at most the leading-order contribution to the logarithmic singular term was extracted from the kernel and treated analytically, the higher-order singular derivatives were left untreated, and the resulting integration methods for the kernel exhibit $\\mathcal{O}(M^{-3})$ convergence at best. A rather comprehensive set of tests we consider shows that, in many cases, to achieve a given accuracy, the numbers $N$ of unknowns required by our codes are up to a factor of five times smaller than those required by the best solvers previously available; the required number $M$ of integration points, in turn, can be several orders of magnitude smaller than those required in previous methods. In particular, four-digit solutions were found in computational times of the order of four seconds and, in most cases, of the order of a fraction of a second on a contemporary personal computer; much higher accuracies result in very small additional computing times.", "date": "2007-06-12", "date_type": "published", "publication": "SIAM Journal on Scientific Computing", "volume": "29", "number": "4", "publisher": "SIAM Journal on Scientific Computing", "pagerange": "1375-1402", "id_number": "CaltechAUTHORS:BRUsiamjsc07", "issn": "1064-8275", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:BRUsiamjsc07", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "doi": "10.1137/050648262", "primary_object": { "basename": "BRUsiamjsc07.pdf", "url": "https://authors.library.caltech.edu/records/nygc5-wbj85/files/BRUsiamjsc07.pdf" }, "resource_type": "article", "pub_year": "2007", "author_list": "Bruno, Oscar P. and Haslam, Michael C." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/nhp15-23v60", "eprint_id": 90649, "eprint_status": "archive", "datestamp": "2023-08-22 08:03:14", "lastmod": "2023-10-19 14:43:12", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Amundsen-D-E", "name": { "family": "Amundsen", "given": "David E." } }, { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar" }, "orcid": "0000-0001-8369-3014" } ] }, "title": "Time Stepping Via One-Dimensional Pad\u00e9 Approximation", "ispublished": "pub", "full_text_status": "restricted", "keywords": "Numerical solution; explicit methods; evolution partial differential equations; stiff ordinary differential equations; Pad\u00e9 time stepping (PTS)", "note": "\u00a9 2005 Springer Science+Business Media, Inc. \n\nReceived August 11, 2005; accepted (in revised form) October 14, 2005; Published online December 28, 2005. \n\nThe authors wish to acknowledge useful conversations with Mike\nGiles, Jan Hesthaven and Lee Lindblom, whose independent tests of the PTS method gave rise important insights on the algorithm. DEA gratefully acknowledges support from NSERC Discovery Grant 249732-02 and Canada Foundation for Innovation New Opportunities Grant 7361. OB thankfully acknowledges support from the Air Force Office of Scientific Research, Air Force Materials Command, USAF, under grant numbers F49620-99-1-0010 and F49620-02-1-0049, and from the NSF under contracts number DMS-9816802 and DMS-0104531. The US Government is authorized to reproduce and distribute reprints for governmental purposes notwithstanding any copyright notation thereon. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of the Air Force Office of Scientific Research or the US Government.", "abstract": "The numerical solution of time-dependent ordinary and partial differential equations presents a number of well known difficulties\u2014including, possibly, severe restrictions on time-step sizes for stability in explicit procedures, as well as need for solution of challenging, generally nonlinear systems of equations in implicit schemes. In this note we introduce a novel class of explicit methods based on use of one-dimensional Pad\u00e9 approximation. These schemes, which are as simple and inexpensive per time-step as other explicit algorithms, possess, in many cases, properties of stability similar to those offered by implicit approaches. We demonstrate the character of our schemes through application to notoriously stiff systems of ODEs and PDEs. In a number of important cases, use of these algorithms has resulted in orders-of-magnitude reductions in computing times over those required by leading approaches.", "date": "2007-01", "date_type": "published", "publication": "Journal of Scientific Computing", "volume": "30", "number": "1", "publisher": "Springer", "pagerange": "83-115", "id_number": "CaltechAUTHORS:20181105-143029068", "issn": "0885-7474", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20181105-143029068", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Natural Sciences and Engineering Research Council of Canada (NSERC)", "grant_number": "249732-02" }, { "agency": "Canada Foundation for Innovation", "grant_number": "7361" }, { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "F49620-99-1-0010" }, { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "F49620-02-1-0049" }, { "agency": "NSF", "grant_number": "DMS-9816802" }, { "agency": "NSF", "grant_number": "DMS-0104531" } ] }, "doi": "10.1007/s10915-005-9021-4", "resource_type": "article", "pub_year": "2007", "author_list": "Amundsen, David E. and Bruno, Oscar" }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/w3hxg-szc24", "eprint_id": 432, "eprint_status": "archive", "datestamp": "2023-08-22 03:44:21", "lastmod": "2023-10-13 21:48:38", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar P." }, "orcid": "0000-0001-8369-3014" }, { "id": "Hyde-E-M", "name": { "family": "Hyde", "given": "E. McKay" } } ] }, "title": "Higher-Order Fourier Approximation in Scattering by Two-Dimensional, Inhomogeneous Media", "ispublished": "pub", "full_text_status": "public", "keywords": "Helmholtz equation, Lippmann-Schwinger integral equation, transverse electric scattering, TM scattering, fast Fourier transform", "note": "\u00a9 2005 Society for Industrial and Applied Mathematics. \n\nReceived by the editors April 7, 2003; accepted for publication (in revised form) March 25, 2004; published electronically March 31, 2005. This effort was sponsored in part by the Air Force Office of Scientific Research (AFOSR), Air Force Materials Command, USAF, under the AASERT award F49620-98-1-0368. The U.S. Government is authorized to reproduce and distribute reprints for governmental purposes notwithstanding any copyright notation thereon. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of the Air Force Office of Scientific Research or the U.S. Government. \n\nThe research of [Oscar P. Bruno] was supported by AFOSR grants F49620-96-1-0008, F49620-99-1-0010, and F49620-02-1-0049; the NSF through the NYI award DMS-9596152 and through contracts DMS-9523292, DMS-9816802, and DMS-0104531; and the Powell Research Foundation. The research of [E. McKay Hyde] was supported by a DOE Computational Science Graduate Fellowship, an Achievement Rewards for College Scientists (ARCS) Fellowship, and an NSF Mathematical Sciences Postdoctoral Research Fellowship. \n\nColor visualizations were generated with the VTK-based visualization tool Vizamrai, developed by Steven Smith at the Center for Applied Scientific Computing (CASC) at Lawrence Livermore National Laboratory. The authors also gratefully acknowledge the constructive suggestions of an anonymous referee.", "abstract": "This paper provides a theoretical analysis of a higher-order, FFT-based integral equation method introduced recently [IEEE Trans. Antennas and Propagation, 48 (2000), pp. 1862-1864] for the evaluation of transverse electric-polarized electromagnetic scattering from a bounded, penetrable inhomogeneity in two-dimensional space. Roughly speaking, this method is based on Fourier smoothing of the integral operator and the refractive index n(x). Here we prove that the solution of the resulting integral equation approximates the solution of the exact integral equation with higher-order accuracy, even when n(x) is a discontinuous function -- as suggested by the numerical experiments contained in the paper mentioned above. In detail, we relate the convergence rates of the computed interior and exterior fields to the regularity of the scatterer, and we demonstrate, with a few numerical examples, that the predicted convergence rates are achieved in practice.", "date": "2005-06-01", "date_type": "published", "publication": "SIAM Journal on Numerical Analysis", "volume": "42", "number": "6", "publisher": "SIAM Journal on Numerical Analysis", "pagerange": "2298-2319", "id_number": "CaltechAUTHORS:BRUsiamjna05", "issn": "0036-1429", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:BRUsiamjna05", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "doi": "10.1137/S0036142903425811", "primary_object": { "basename": "BRUsiamjna05.pdf", "url": "https://authors.library.caltech.edu/records/w3hxg-szc24/files/BRUsiamjna05.pdf" }, "resource_type": "article", "pub_year": "2005", "author_list": "Bruno, Oscar P. and Hyde, E. McKay" }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/qydfz-r7v63", "eprint_id": 369, "eprint_status": "archive", "datestamp": "2023-08-22 03:35:51", "lastmod": "2023-10-13 20:39:09", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Geuzaine-C", "name": { "family": "Geuzaine", "given": "Christophe" } }, { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar" }, "orcid": "0000-0001-8369-3014" }, { "id": "Reitich-F", "name": { "family": "Reitich", "given": "Fernando" } } ] }, "title": "On the O(1) Solution of Multiple-Scattering Problems", "ispublished": "pub", "full_text_status": "public", "keywords": "Wave scattering, boundary integral equations, spectral methods, high-frequency methods", "note": "\"\u00a92005 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.\" \n\nManuscript received June 8, 2004. \n\nThis work was supported in part by the Air Force Office of Scientific Research, the Defense Advanced Research Projects Agency, the Army High Performance Computing Research Center, the National Science Foundation, and the Belgian Science Policy (P5/34).", "abstract": "In this paper, we present a multiple-scattering solver for nonconvex geometries such as those obtained as the union of a finite number of convex surfaces. For a prescribed error tolerance, this algorithm exhibits a fixed computational cost for arbitrarily high frequencies. At the core of the method is an extension of the method of stationary phase, together with the use of an ansatz for the unknown density in a combined-field boundary integral formulation.", "date": "2005-05-01", "date_type": "published", "publication": "IEEE Transactions on Magnetics", "volume": "41", "number": "5", "publisher": "IEEE Transactions on Magnetics", "pagerange": "1488-1491", "id_number": "CaltechAUTHORS:GEUieeetm05.862", "issn": "0018-9464", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:GEUieeetm05.862", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "doi": "10.1109/TMAG.2005.844567", "primary_object": { "basename": "GEUieeetm05.pdf", "url": "https://authors.library.caltech.edu/records/qydfz-r7v63/files/GEUieeetm05.pdf" }, "resource_type": "article", "pub_year": "2005", "author_list": "Geuzaine, Christophe; Bruno, Oscar; et el." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/kve0z-tzn28", "eprint_id": 455, "eprint_status": "archive", "datestamp": "2023-08-22 03:23:52", "lastmod": "2023-10-13 21:49:25", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "O." }, "orcid": "0000-0001-8369-3014" }, { "id": "Chaubell-J", "name": { "family": "Chaubell", "given": "J." } } ] }, "title": "One-dimensional inverse scattering problem for optical coherence tomography", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2005 IOP Publishing Ltd. \n\nReceived 13 February 2004, in final form 4 January 2005, Published 23 February 2005, Print publication: Issue 2 (April 2005).", "abstract": "Optical coherence tomography is a non-invasive imaging technique based on the use of light sources exhibiting a low degree of coherence. Low-coherence interferometric microscopes have been successful in producing internal images of thin pieces of biological tissue; typically samples of the order of 1 mm in depth have been imaged, with a resolution of the order of 10 \u00b5m in some portions of the sample. In this paper we deal with the imaging problem of determining the internal structure of a multi-layered sample from backscattered laser light and low-coherence interferometry. In detail, we formulate and solve an inverse problem which, using the interference fringes that result as the back scattering of low-coherence light is made to interfere with a reference beam, produces maps detailing the values of the refractive index within the imaged sample. Unlike previous approaches to the OCT imaging problem, the method we introduce does not require processing at data collection time, and it produces quantitatively accurate values of the refractive indexes within the sample from back-scattering interference fringes only.", "date": "2005-04", "date_type": "published", "publication": "Inverse Problems", "volume": "21", "number": "2", "publisher": "IOP", "pagerange": "499-524", "id_number": "CaltechAUTHORS:BRUip05", "issn": "0266-5611", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:BRUip05", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "doi": "10.1088/0266-5611/21/2/006", "primary_object": { "basename": "BRUip05.pdf", "url": "https://authors.library.caltech.edu/records/kve0z-tzn28/files/BRUip05.pdf" }, "resource_type": "article", "pub_year": "2005", "author_list": "Bruno, O. and Chaubell, J." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/kktvf-c6684", "eprint_id": 90593, "eprint_status": "archive", "datestamp": "2023-08-22 03:01:35", "lastmod": "2023-10-19 14:37:08", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Hyde-E-M", "name": { "family": "Hyde", "given": "E. McKay" } }, { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar P." }, "orcid": "0000-0001-8369-3014" } ] }, "title": "A fast, higher-order solver for scattering by penetrable bodies in three dimensions", "ispublished": "pub", "full_text_status": "restricted", "keywords": "Helmholtz equation; Lippmann\u2013Schwinger equation; Fourier series; Fast Fourier transform; High-order quadrature", "note": "\u00a9 2004 Elsevier Inc.\n\nReceived 31 October 2003, Revised 22 June 2004, Accepted 8 July 2004, Available online 26 August 2004. \n\nThe original implementation of the method described in the appendix (for computing the Fourier coefficients of the singular part of the Green's function) was written at Caltech by Samba Ba, a visiting undergraduate from \u00c9cole Polytechnique, France. Color visualizations of the scatterers and the near field intensities were generated with the VTK-based visualization tool Vizamrai, developed by Steven Smith at the Center for Applied Scientific Computing (CASC) at Lawrence Livermore National Laboratory. Far field visualizations were created with SceneViewer, a 3D viewer for Open Inventor scenes; the scene graph files were generated with software written by Randy Paffenroth at Caltech. \n\nSupported through a DOE Computational Science Graduate Fellowship, an Achievement Rewards for College Scientists (ARCS) Fellowship and an NSF Mathematical Sciences Postdoctoral Research Fellowship. \n\nSupported by the AFOSR under grant numbers F49620-96-1-0008, F49629-99-1-0010 and F49620-02-10049, by the NSF through the NYI award DMS-9596152 and contracts No. DMS-9523292, DMS-9816802 and DMS-0104531 and by the Powell Research Foundation.", "abstract": "In this paper, we introduce a new fast, higher-order solver for scattering by inhomogeneous media in three dimensions. As in previously existing methods, the low complexity of our integral equation method, O(N log N) operations for an N point discretization, is obtained through extensive use of the fast Fourier transform (FFT) for the evaluation of convolutions. However, the present approach obtains significantly higher-order accuracy than these previous approaches, yielding, at worst, third-order far field accuracy (or substantially better for smooth scatterers), even for discontinuous and complex refractive index distributions (possibly containing severe geometric singularities such as corners and cusps). The increased order of convergence of our method results from (i) a partition of unity decomposition of the Green's function into a smooth part with unbounded support and a singular part with compact support, and (ii) replacement of the (possibly discontinuous) scatterer by an appropriate \"Fourier smoothed\" scatterer; the resulting convolutions can then be computed with higher-order accuracy by means of O(N log N) FFTs. We present a parallel implementation of our approach, and demonstrate the method's efficiency and accuracy through a variety of computational examples. For a very large scatterer considered earlier in the literature (with a volume of 3648\u03bb3, where \u03bb is the wavelength), using the same number of points per wavelength and in computing times comparable to those required by the previous approach, the present algorithm produces far-field values whose errors are two orders of magnitude smaller than those reported previously.", "date": "2005-01-01", "date_type": "published", "publication": "Journal of Computational Physics", "volume": "202", "number": "1", "publisher": "Elsevier", "pagerange": "236-261", "id_number": "CaltechAUTHORS:20181101-152904320", "issn": "0021-9991", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20181101-152904320", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)" }, { "agency": "ARCS Foundation" }, { "agency": "NSF Postdoctoral Fellowship" }, { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "F49620-96-1-0008" }, { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "F49629-99-1-0010" }, { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "F49620-02-10049" }, { "agency": "NSF", "grant_number": "DMS-9596152" }, { "agency": "NSF", "grant_number": "DMS-9523292" }, { "agency": "NSF", "grant_number": "DMS-9816802" }, { "agency": "NSF", "grant_number": "DMS-0104531" }, { "agency": "Charles Lee Powell Foundation" } ] }, "doi": "10.1016/j.jcp.2004.07.006", "resource_type": "article", "pub_year": "2005", "author_list": "Hyde, E. McKay and Bruno, Oscar P." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/ns1e5-ax435", "eprint_id": 90592, "eprint_status": "archive", "datestamp": "2023-08-22 02:40:42", "lastmod": "2023-10-19 14:37:02", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar P." }, "orcid": "0000-0001-8369-3014" }, { "id": "Hyde-E-M", "name": { "family": "Hyde", "given": "E. McKay" } } ] }, "title": "An efficient, preconditioned, high-order solver for scattering by two-dimensional inhomogeneous media", "ispublished": "pub", "full_text_status": "restricted", "keywords": "Helmholtz equation; Lippmann\u2013Schwinger equation; FFT; TE/TM scattering; Preconditioner; Chebyshev polynomials; Bessel functions", "note": "\u00a9 2004 Elsevier. \n\nReceived 31 October 2003, Revised 29 April 2004, Accepted 29 April 2004, Available online 8 June 2004. \n\nColor visualizations generated with the VTK-based visualization tool Vizamrai, developed by Steven Smith at the Center for Applied Scientific Computing (CASC), Lawrence Livermore National Laboratory. \n\nSupported by the AFOSR under Grant Nos. F49620-96-1-0008, F49629-99-1-0010 and F49620-02-10049, by the NSF through the NYI award DMS-9596152 and contract Nos. DMS-9523292, DMS-9816802 and DMS-0104531 and by the Powell Research Foundation.\n\nSupported through a DOE Computational Science Graduate Fellowship, an Achievement Reward for College Scientists (ARCS) Fellowship and an NSF Mathematical Sciences Postdoctoral Research Fellowship.", "abstract": "We consider the problem of evaluating the scattering of TE polarized electromagnetic waves by two-dimensional penetrable inhomogeneities: building upon previous work [IEEE Trans. Antennas Propag. 48 (2000) 1862] we present a practical and general fast integral equation algorithm for this problem. The contributions introduced in this text include: (1) a preconditioner that significantly reduces the number of iterations required by the algorithm in the treatment of electrically large scatterers, (2) a new radial integration scheme based on Chebyshev polynomial approximation, which gives rise to increased accuracy, efficiency and stability, and (3) an efficient and stable method for the evaluation of scaled high-order Bessel functions, which extends the capabilities of the method to arbitrarily high frequencies. These enhancements give rise to an algorithm that is much more accurate and efficient than its previous counterpart, and that allows for treatment of much larger problems than permitted by the previous approach. In one test case, for example, the present algorithm results in far-field errors of 8.9\u00d710^(\u221213) in a 2.12s calculation (on a 1.7 GHz PC) whereas the original algorithm gave rise to far-field errors of 1.1\u00d710^(\u22128) in 88.91s on a 400 MHz PC. In another example, the present algorithm evaluates accurately the scattering by a cylinder of acoustical size \u03baR=256, which is of the order of 20 times larger (400 times larger in square wavelengths) than the largest scatterers that could be treated by the previous approach. Yielding, at worst, third-order far field accuracy (or substantially better, for smooth scatterers) in fast computing times (O(N log N) operations for an N point mesh) even for discontinuous and complex refractive index distributions (possibly containing severe geometric singularities such as corners and cusps), the proposed approach is the highest-order O(N log N) solver in existence for the problem under consideration.", "date": "2004-11-01", "date_type": "published", "publication": "Journal of Computational Physics", "volume": "200", "number": "2", "publisher": "Elsevier", "pagerange": "670-694", "id_number": "CaltechAUTHORS:20181101-152904227", "issn": "0021-9991", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20181101-152904227", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "F49620-96-1-0008" }, { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "F49629-99-1-0010" }, { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "F49620-02-10049" }, { "agency": "NSF", "grant_number": "DMS-9596152" }, { "agency": "NSF", "grant_number": "DMS-9523292" }, { "agency": "NSF", "grant_number": "DMS-9816802" }, { "agency": "NSF", "grant_number": "DMS-0104531" }, { "agency": "Charles Lee Powell Foundation" }, { "agency": "Department of Energy (DOE)" }, { "agency": "ARCS Foundation" }, { "agency": "NSF Postdoctoral Fellowship" } ] }, "doi": "10.1016/j.jcp.2004.04.017", "resource_type": "article", "pub_year": "2004", "author_list": "Bruno, Oscar P. and Hyde, E. McKay" }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/fzgq3-w0c71", "eprint_id": 75884, "eprint_status": "archive", "datestamp": "2023-08-22 02:03:11", "lastmod": "2023-10-25 15:23:15", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Goldsztein-G-H", "name": { "family": "Goldsztein", "given": "Guillermo H." } }, { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar P." }, "orcid": "0000-0001-8369-3014" } ] }, "title": "A fast algorithm for the simulation of polycrystalline misfits. II. Martensitic transformations in three space dimensions", "ispublished": "pub", "full_text_status": "restricted", "keywords": "phase transformation; polycrystalline material; numerical algorithms; homogenization", "note": "\u00a9 2004 The Royal Society. \n\nReceived 24 April 2003; accepted 11 August 2003; published online 9 March 2004. \n\nThis work was sponsored by the Air Force Office of Scientific Research, Air Force Materials Command, USAF, under grant numbers F49620-96-1-0008 and F49620-99-1-0010. The authors gratefully acknowledge support from NSF (through an NYI award). O.P.B. gratefully acknowledges support from NSF (through contract numbers DMS-9523292 and DMS-9816802) and from the Powell Research Foundation. The US Government is authorized to reproduce and distribute reprints for governmental purposes notwithstanding any copyright notation thereon. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of the Air Force Office of Scientific Research or the US Government.", "abstract": "We present a fast numerical method for the simulation of martensitic transformations in three\u2013dimensional polycrystals. To produce the relevant overall elastic energy arising from given boundary conditions, this method proceeds by reducing the corresponding non\u2013convex minimization problem to minimization of a certain quadratic form\u2014over the set of arrays of transformation strains which are compatible with a given distribution of crystallite orientations. The evaluation of this quadratic form for a given array of transformation strains requires solution of certain linear elasticity problems. An acceleration strategy we use, which for a polycrystal containing N grains reduces the complexity of the algorithm from O(N^2) to O(N) operations, results from a formulation of the minimization problem which takes advantage of certain decorrelations present in the minimizing arrays of transformation strains. We illustrate our presentation with a number of examples involving cubic\u2013to\u2013monoclinic and cubic\u2013to\u2013orthorhombic polycrystalline phase transitions, such as those arising in the TiNi and CuAl shape\u2013memory alloys. In particular, our study quantifies the effects of texture on the overall properties of such polycrystalline shape\u2013memory alloys.", "date": "2004-06-08", "date_type": "published", "publication": "Proceedings of the Royal Society A: Mathematical, physical, and engineering sciences", "volume": "460", "number": "2046", "publisher": "Royal Society of London", "pagerange": "1613-1630", "id_number": "CaltechAUTHORS:20170408-135429636", "issn": "1364-5021", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170408-135429636", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "F49620-96-1-0008" }, { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "49620-99-1-0010" }, { "agency": "NSF", "grant_number": "DMS-9523292" }, { "agency": "NSF", "grant_number": "DMS-9816802" }, { "agency": "Charles Lee Powell Foundation" } ] }, "doi": "10.1098/rspa.2003.1223", "resource_type": "article", "pub_year": "2004", "author_list": "Goldsztein, Guillermo H. and Bruno, Oscar P." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/cycy8-gbg97", "eprint_id": 90679, "eprint_status": "archive", "datestamp": "2023-08-22 01:42:40", "lastmod": "2023-10-19 14:46:04", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar P." }, "orcid": "0000-0001-8369-3014" }, { "id": "Geuzaine-C-A", "name": { "family": "Geuzaine", "given": "Christophe A." } }, { "id": "Monro-J-A-Jr", "name": { "family": "Monro", "given": "John A., Jr." } }, { "id": "Reitich-F", "name": { "family": "Reitich", "given": "Fernando" } } ] }, "title": "Prescribed error tolerances within fixed computational times for scattering problems of arbitrarily high frequency: the convex case", "ispublished": "pub", "full_text_status": "restricted", "keywords": "wave scattering; boundary-integral equations; spectral methods; high-frequency methods", "note": "\u00a9 2004 The Royal Society. \n\nPublished online 21 January 2004. \n\nOne contribution of 13 to a Theme 'Short-wave scattering'. \n\nThe efforts of O.B. and C.G. were sponsored by the Air Force Office of Scientific Research, Air Force Materials Command, USAF, under grant nos F49620-99-1-0010 and F49620-02-1-0049. Support from the NSF under contract nos DMS-9816802 and DMS-0104531 and from the Powell Research Foundation is gratefully acknowledged. C.G. is an FNRS Postdoctoral Scholar with the Montefiore Department, University of Li\u00e8ge, Belgium. The efforts of F.R. were sponsored by the Air Force Office of Scientific Research, Air Force Materials Command, USAF, under grant no. F49620-02-1-0052, by the NSF through grant nos DMS-9971379 and DMS-0311763, and by Army High Performance Computing Research Center (AHPCRC) under the auspices of the Department of the Army, Army Research Laboratory cooperative agreement no. DAAD19-01-2-0014. The US Government is authorized to reproduce and distribute reprints for governmental purposes notwithstanding any copyright notation thereon. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of the Air Force Office of Scientific Research or the US Government.", "abstract": "We present a new algorithm for the numerical solution of problems of electromagnetic or acoustic scattering by large, convex obstacles. This algorithm combines the use of an ansatz for the unknown density in a boundary-integral formulation of the scattering problem with an extension of the ideas of the method of stationary phase. We include numerical results illustrating the high-order convergence of our algorithm as well as its asymptotically bounded computational cost as the frequency increases.", "date": "2004-03-15", "date_type": "published", "publication": "Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences", "volume": "362", "number": "1816", "publisher": "Royal Society", "pagerange": "629-645", "id_number": "CaltechAUTHORS:20181106-150424948", "issn": "1364-503X", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20181106-150424948", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "F49620-99-1-0010" }, { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "F49620-02-1-0049" }, { "agency": "NSF", "grant_number": "DMS-9816802" }, { "agency": "NSF", "grant_number": "DMS-0104531" }, { "agency": "Charles Lee Powell Foundation" }, { "agency": "Fonds de la Recherche Scientifique (FNRS)" }, { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "F49620-02-1-0052" }, { "agency": "NSF", "grant_number": "DMS-9971379" }, { "agency": "NSF", "grant_number": "DMS-0311763" }, { "agency": "Army Research Laboratory (ARL)", "grant_number": "DAAD19-01-2-0014" } ] }, "doi": "10.1098/rsta.2003.1338", "resource_type": "article", "pub_year": "2004", "author_list": "Bruno, Oscar P.; Geuzaine, Christophe A.; et el." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/x1j6y-q8022", "eprint_id": 90623, "eprint_status": "archive", "datestamp": "2023-08-19 12:49:19", "lastmod": "2023-10-19 14:38:23", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar P." }, "orcid": "0000-0001-8369-3014" } ] }, "title": "New high-order integral methods in computational electromagnetism", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2004 Tech Science Press.\n\nPublished - cmes.2004.005.319.pdf
", "abstract": "We present a new set of high-order algorithms and methodologies for the numerical solution of problems of scattering by complex bodies in three-dimensional space. These methods, which are based on integral equations, high-order integration and Fast Fourier Transforms, can be used in the solution of problems of electromagnetic and acoustic scattering by surfaces and penetrable scatterers\u2014even in cases in which the scatterers contain geometric singularities such as corners and edges. The solvers presented here exhibit high-order convergence, they run on low memories and reduced operation counts, and they result in solutions with a high degree of accuracy.", "date": "2004", "date_type": "published", "publication": "CMES: Computer Modeling in Engineering and Sciences", "volume": "5", "number": "4", "publisher": "Tech Science Press", "pagerange": "319-330", "id_number": "CaltechAUTHORS:20181102-161613781", "issn": "1526-1492", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20181102-161613781", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "doi": "10.3970/cmes.2004.005.319", "primary_object": { "basename": "cmes.2004.005.319.pdf", "url": "https://authors.library.caltech.edu/records/x1j6y-q8022/files/cmes.2004.005.319.pdf" }, "resource_type": "article", "pub_year": "2004", "author_list": "Bruno, Oscar P." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/mwm6z-4w410", "eprint_id": 90652, "eprint_status": "archive", "datestamp": "2023-08-22 01:20:55", "lastmod": "2024-01-14 21:09:02", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Geronimo-J-S", "name": { "family": "Geronimo", "given": "Jeffrey S." } }, { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar" }, "orcid": "0000-0001-8369-3014" }, { "id": "Van-Assche-W", "name": { "family": "Van Assche", "given": "Walter" } } ] }, "title": "WKB and Turning Point Theory for Second-order Difference Equations", "ispublished": "unpub", "full_text_status": "restricted", "keywords": "Turning point; difference equations; WKB; orthogonal polynomials; hermite polynomials", "note": "\u00a9 2004 Springer Basel AG. \n\nJ.S.G. was supported by NSF grants. J.S.G. and W.V.A. were supported by a NATO grant. \n\nJ.S.G. would like to thank K. McLaughlin, and P. Miller for discussion pertaining to the matching problem S. Garoufalidis for comments regarding the introduction, A. Martinez Finkelstein for pointing out reference [WW], and F. Olver for discussion pertaining to Airy and Hankel functions in the complex plane.", "abstract": "A turning point method for difference equations is developed. This method is coupled with the LG-WKB method via matching to provide approximate solutions to the initial value problem. The techniques developed are used to provide strong asymptotics for Hermite polynomials.", "date": "2004", "date_type": "published", "publisher": "Birkh\u00e4user", "place_of_pub": "Basel", "pagerange": "101-138", "id_number": "CaltechAUTHORS:20181105-153010735", "isbn": "978-3-0348-9632-0", "book_title": "Spectral Methods for Operators of Mathematical Physics", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20181105-153010735", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF" }, { "agency": "North Atlantic Treaty Organization (NATO)" } ] }, "contributors": { "items": [ { "id": "Janas-J", "name": { "family": "Janas", "given": "Jan" } }, { "id": "Kurasov-P", "name": { "family": "Kurasov", "given": "Pavel" } }, { "id": "Naboko-S", "name": { "family": "Naboko", "given": "Sergei" } } ] }, "doi": "10.1007/978-3-0348-7947-7_7", "resource_type": "book_section", "pub_year": "2004", "author_list": "Geronimo, Jeffrey S.; Bruno, Oscar; et el." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/mv8vd-4ys81", "eprint_id": 2915, "eprint_status": "archive", "datestamp": "2023-08-22 01:05:17", "lastmod": "2023-10-13 23:48:33", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar P." }, "orcid": "0000-0001-8369-3014" }, { "id": "Chaubell-J", "name": { "family": "Chaubell", "given": "Julian" } } ] }, "title": "Inverse scattering problem for optical coherence tomography", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2003 Optical Society of America \n\nReceived May 29, 2003 \n\nSupport provided by TRW, the U.S. Air Force Office of Scientific Research, and the National Science Foundation is gratefully acknowledged.", "abstract": "We deal with the imaging problem of determining the internal structure of a body from backscattered laser light and low-coherence interferometry. Specifically, using the interference fringes that result when the backscattering of low-coherence light is made to interfere with the reference beam, we obtain maps detailing the values of the refractive index within the sample. Our approach accounts fully for the statistical nature of the coherence phenomenon; the numerical experiments that we present, which show image reconstructions of high quality, were obtained under noise floors exceeding those present for various experimental setups reported in the literature.", "date": "2003-11-01", "date_type": "published", "publication": "Optics Letters", "volume": "28", "number": "21", "publisher": "Optics Letters", "pagerange": "2049-2051", "id_number": "CaltechAUTHORS:BRUol03", "issn": "0146-9592", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:BRUol03", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "primary_object": { "basename": "BRUol03.pdf", "url": "https://authors.library.caltech.edu/records/mv8vd-4ys81/files/BRUol03.pdf" }, "resource_type": "article", "pub_year": "2003", "author_list": "Bruno, Oscar P. and Chaubell, Julian" }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/vtdfc-y2124", "eprint_id": 1281, "eprint_status": "archive", "datestamp": "2023-08-22 01:02:20", "lastmod": "2023-10-13 22:43:28", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar P." }, "orcid": "0000-0001-8369-3014" }, { "id": "Sei-A", "name": { "family": "Sei", "given": "Alain" } } ] }, "title": "A fast high-order solver for problems of scattering by heterogeneous bodies", "ispublished": "pub", "full_text_status": "public", "keywords": "Electromagnetic scattering, fast algorithms, high-order, inhomogeneous scatterer, penetrable scatterer, Helmholtz equations, electromagnetic wave scattering, integral equations, refractive index", "note": "\"Printed 2003 IEEE. U.S. Government work not protected by U.S. copyright.\" \n\nManuscript received May 25, 1999; revised November 25, 2002. \n\nThis work was supported in part by the Air Force Office of Scientific Research, Air Force Materials Command, USAF, by Grants F49620-96-1-0008, F49620-98-1-0368, F49620-99-1-0010, and F49620-02-1-0049, and by the NSF under Contract numbers DMS-9596152, DMS-9523292, DMS-9816802, and DMS-0104531, and by the Powell Research Foundation. \n\nThe authors wish to thank E. M. Hyde for providing the numerical implementation which was used to produce the tables concerning angular integration.\n\nPublished - BRUieeetap03.pdf
", "abstract": "A new high-order integral algorithm for the solution of scattering problems by heterogeneous bodies is presented. Here, a scatterer is described by a (continuously or discontinuously) varying refractive index n(x) within a two-dimensional (2D) bounded region; solutions of the associated Helmholtz equation under given incident fields are then obtained by high-order inversion of the Lippmann-Schwinger integral equation. The algorithm runs in O(Nlog(N)) operations where N is the number of discretization points. A wide variety of numerical examples provided include applications to highly singular geometries, high-contrast configurations, as well as acoustically/electrically large problems for which supercomputing resources have been used recently. Our method provides highly accurate solutions for such problems on small desktop computers in CPU times of the order of seconds.", "date": "2003-11", "date_type": "published", "publication": "IEEE Transactions on Antennas and Propagation", "volume": "51", "number": "11", "publisher": "IEEE", "pagerange": "3142-3154", "id_number": "CaltechAUTHORS:BRUieeetap03", "issn": "0018-926X", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:BRUieeetap03", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "F49620-96-1-0008" }, { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "F49620-98-1-0368" }, { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "F49620-99-1-0010" }, { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "F49620-02-1-0049" }, { "agency": "NSF", "grant_number": "DMS-9596152" }, { "agency": "NSF", "grant_number": "DMS-9523292" }, { "agency": "NSF", "grant_number": "DMS-9816802" }, { "agency": "NSF", "grant_number": "DMS-0104531" }, { "agency": "Charles Lee Powell Foundation" } ] }, "doi": "10.1109/TAP.2003.818783", "primary_object": { "basename": "BRUieeetap03.pdf", "url": "https://authors.library.caltech.edu/records/vtdfc-y2124/files/BRUieeetap03.pdf" }, "resource_type": "article", "pub_year": "2003", "author_list": "Bruno, Oscar P. and Sei, Alain" }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/5fww3-q9y35", "eprint_id": 90589, "eprint_status": "archive", "datestamp": "2023-09-15 06:10:01", "lastmod": "2023-10-23 21:23:45", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Hyde-E-M", "name": { "family": "Hyde", "given": "E. McKay" } }, { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar P." }, "orcid": "0000-0001-8369-3014" } ] }, "title": "A fast, high-order method for scattering by inhomogeneous media in three dimensions", "ispublished": "pub", "full_text_status": "restricted", "keywords": "Fourier approximation; High-order methods; Integral equations; Scattering by inhomogeneous media", "note": "\u00a9 2003 Elsevier. \n\nAvailable online 7 October 2003. \n\nThis effort was sponsored by the Air Force Office of Scientific Research, Air Force Materials Command, USAF, under Grant Nos. F49620-99-1-0010 and F49620-99-1-0193, DARPA Contract No. F49620-99-C-0014, and through NSF Contracts Nos. DMS-9816802 and DMS-0123292. The US Government is authorized to reproduce and distribute reprints for governmental purposes notwithstanding any copyright notation thereon. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of the Air Force Office of Scientific Research or the US Government. MH gratefully acknowledges support through a DOE Computational Science Graduate Fellowship and an ARCS Foundation Fellowship.", "abstract": "We introduce a new fast, high-order method for scattering by inhomogeneous media in three dimensions. The O(N log N) complexity of our integral equation method is obtained through use of the fast Fourier transform in evaluating the required convolution. High-order convergence is obtained by replacing the scatterer with its truncated Fourier series and by decomposing the Green's function into a smooth part with infinite support and a singular part with compact support. Countering conventional wisdom, this Fourier smoothing of the scatterer yields high-order convergence, even in the case of discontinuous scatterers. We illustrate the performance of our parallel implementation of this method through two computational examples.", "date": "2003-10", "date_type": "published", "publication": "Physica B", "volume": "338", "number": "1-4", "publisher": "Elsevier", "pagerange": "82-86", "id_number": "CaltechAUTHORS:20181101-152903960", "issn": "0921-4526", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20181101-152903960", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "F49620-99-1-0010" }, { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "F49620-99-1-0193" }, { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "F49620-99-C-0014" }, { "agency": "Defense Advanced Research Projects Agency (DARPA)" }, { "agency": "NSF", "grant_number": "DMS-9816802" }, { "agency": "NSF", "grant_number": "DMS-0123292" }, { "agency": "Department of Energy (DOE)" }, { "agency": "ARCS Foundation" } ] }, "doi": "10.1016/s0921-4526(03)00465-4", "resource_type": "article", "pub_year": "2003", "author_list": "Hyde, E. McKay and Bruno, Oscar P." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/8s437-0wf61", "eprint_id": 90594, "eprint_status": "archive", "datestamp": "2023-09-15 06:10:10", "lastmod": "2023-10-23 21:23:47", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar P." }, "orcid": "0000-0001-8369-3014" } ] }, "title": "Wave scattering by inhomogeneous media: efficient algorithms and applications", "ispublished": "pub", "full_text_status": "restricted", "keywords": "EM scattering; Fast algorithms; High-order accuracy; High-frequency", "note": "\u00a9 2003 Elsevier. \n\nAvailable online 5 September 2003. \n\nEffort sponsored by the Air Force Office of Scientific Research, Air Force Materials Command, USAF, under Grant Nos. F49620-99-1-0010 and F49620-99-1-0193, DARPA Contract No. F49620-99-C-0014, and through NSF Contract Nos. DMS-9816802 and DMS-0123292. The US Government is authorized to reproduce and distribute reprints for governmental purposes notwithstanding any copyright notation thereon. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of the Air Force Office of Scientific Research or the US Government.", "abstract": "We review a new set of algorithms and methodologies for the numerical solution of problems of scattering by complex bodies in three-dimensional space. These methods, which are based on integral equations, high-order integration, fast Fourier transforms and highly accurate high-frequency methods, can be used in the solution of problems of electromagnetic and acoustic scattering by surfaces\u2014even in cases in which the scatterers contain geometric singularities such as corners and edges. In all cases, the solvers exhibit high-order convergence, they run on low memories and reduced operation counts, and they result in solutions with a high degree of accuracy. A class of high-order high-frequency methods currently under development, in turn, are efficient where our direct methods become costly, and they thus lead to an overall computational methodology which is applicable and accurate throughout the electromagnetic spectrum.", "date": "2003-10", "date_type": "published", "publication": "Physica B", "volume": "338", "number": "1-4", "publisher": "Elsevier", "pagerange": "67-73", "id_number": "CaltechAUTHORS:20181101-152904409", "issn": "0921-4526", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20181101-152904409", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "F49620-99-1-0010" }, { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "F49620-99-1-0193" }, { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "F49620-99-C-0014" }, { "agency": "Defense Advanced Research Projects Agency (DARPA)" }, { "agency": "NSF", "grant_number": "DMS-9816802" }, { "agency": "NSF", "grant_number": "DMS-0123292" } ] }, "doi": "10.1016/s0921-4526(03)00462-9", "resource_type": "article", "pub_year": "2003", "author_list": "Bruno, Oscar P." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/4a9rf-0b071", "eprint_id": 90655, "eprint_status": "archive", "datestamp": "2023-08-22 00:01:24", "lastmod": "2024-01-14 21:09:05", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar P." }, "orcid": "0000-0001-8369-3014" } ] }, "title": "Fast, High-Order, High-Frequency Integral Methods for Computational Acoustics and Electromagnetics", "ispublished": "unpub", "full_text_status": "restricted", "keywords": "Fourier Series; Trapezoidal Rule; Helmholtz Equation; Singular Surface; Fast Multipole Method", "note": "\u00a9 2003 Springer-Verlag Berlin Heidelberg.", "abstract": "We review a set of algorithms and methodologies developed recently for the numerical solution of problems of scattering by complex bodies in three-dimensional space. These methods, which are based on integral equations, high-order integration, Fast Fourier Transforms and highly accurate high-frequency integrators, can be used in the solution of problems of electromagnetic and acoustic scattering by surfaces and penetrable scatterers \u2014 even in cases in which the scatterers contain geometric singularities such as comers and edges. All of the solvers presented here exhibit high-order convergence, they run on low memories and reduced operation counts, and they result in solutions with a high degree of accuracy. In particular, our approach to direct solution of integral equations results in algorithms that can evaluate accurately in a personal computer scattering from hundred-wavelength-long objects \u2014 a goal, otherwise achievable today only by super-computing. The high-order high-frequency methods we present, in turn, are efficient where our direct methods become costly, thus leading to an overall computational methodology which is applicable and accurate throughout the electromagnetic spectrum.", "date": "2003", "date_type": "published", "publisher": "Springer", "place_of_pub": "Berlin", "pagerange": "43-82", "id_number": "CaltechAUTHORS:20181106-073820064", "isbn": "978-3-540-00744-9", "book_title": "Topics in Computational Wave Propagation: Direct and Inverse Problems", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20181106-073820064", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "contributors": { "items": [ { "id": "Ainsworth-M", "name": { "family": "Ainsworth", "given": "Mark" } }, { "id": "Davies-P", "name": { "family": "Davies", "given": "Penny" } }, { "id": "Duncan-D", "name": { "family": "Duncan", "given": "Dugald" } }, { "id": "Rynne-B", "name": { "family": "Rynne", "given": "Bryan" } }, { "id": "Martin-P", "name": { "family": "Martin", "given": "Paul" } } ] }, "doi": "10.1007/978-3-642-55483-4_2", "resource_type": "book_section", "pub_year": "2003", "author_list": "Bruno, Oscar P." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/z0v9w-c7d75", "eprint_id": 50833, "eprint_status": "archive", "datestamp": "2023-08-19 09:51:43", "lastmod": "2023-10-18 14:34:14", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar P." }, "orcid": "0000-0001-8369-3014" }, { "id": "Sei-A", "name": { "family": "Sei", "given": "Alain" } }, { "id": "Caponi-M", "name": { "family": "Caponi", "given": "Maria" } } ] }, "title": "High-order high-frequency solutions of rough surface scattering problems", "ispublished": "pub", "full_text_status": "public", "keywords": "scattering, rough surface, high frequency, numerical methods, integral equations", "note": "Copyright 2002 by the American Geophysical Union. \n\nReceived 30 August 2000; revised 12 October 2001; accepted 6 February 2002; published 11 July 2002. \n\nThis effort was sponsored by DARPA/AFOSR under contract F49620-99-C-0014, by the Air Force Office of Scientific Research, Air Force Materials Command, USAF, under grants F49620-99-1-0010 and F49620-99-1-0193, and through NSF contracts DMS-9523292 and DMS-9816802. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of the Air Force Office of Scientific Research or the U.S. Government.\n\nPublished - rds4656.pdf
Supplemental Material - rds4656-sup-0001-tab01.txt
Supplemental Material - rds4656-sup-0002-tab02.txt
Supplemental Material - rds4656-sup-0003-tab03.txt
Supplemental Material - rds4656-sup-0004-tab04.txt
Supplemental Material - rds4656-sup-0005-tab05.txt
Supplemental Material - rds4656-sup-0006-tab06.txt
Supplemental Material - rds4656-sup-0007-tab07.txt
Supplemental Material - rds4656-sup-0008-tab08.txt
Supplemental Material - rds4656-sup-0009-tab09.txt
Supplemental Material - rds4656-sup-0010-tab10.txt
", "abstract": "A new method is introduced for the solution of problems of scattering by rough surfaces in the high-frequency regime. It is shown that high-order summations of expansions in inverse powers of the wave number can be used within an integral equation framework to produce highly accurate results for surfaces and wavelengths of interest in applications. Our algorithm is based on systematic use and manipulation of certain Taylor-Fourier series representations and explicit asymptotic expansions of oscillatory integrals. Results with machine precision accuracy are presented which were obtained from computations involving expansions of order as high as 20.", "date": "2002-08", "date_type": "published", "publication": "Radio Science", "volume": "37", "number": "4", "publisher": "American Geophysical Union", "pagerange": "Art. No. 1049", "id_number": "CaltechAUTHORS:20141027-093609432", "issn": "0048-6604", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20141027-093609432", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Defense Advanced Research Projects Agency (DARPA)" }, { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "F49620-99-C-0014" }, { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "F49620-99-1-0010" }, { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "F49620-99-1-0193" }, { "agency": "NSF", "grant_number": "DMS-9523292" }, { "agency": "NSF", "grant_number": "DMS-9816802" } ] }, "doi": "10.1029/2000RS002551", "primary_object": { "basename": "rds4656-sup-0002-tab02.txt", "url": "https://authors.library.caltech.edu/records/z0v9w-c7d75/files/rds4656-sup-0002-tab02.txt" }, "related_objects": [ { "basename": "rds4656-sup-0005-tab05.txt", "url": "https://authors.library.caltech.edu/records/z0v9w-c7d75/files/rds4656-sup-0005-tab05.txt" }, { "basename": "rds4656-sup-0006-tab06.txt", "url": "https://authors.library.caltech.edu/records/z0v9w-c7d75/files/rds4656-sup-0006-tab06.txt" }, { "basename": "rds4656-sup-0007-tab07.txt", "url": "https://authors.library.caltech.edu/records/z0v9w-c7d75/files/rds4656-sup-0007-tab07.txt" }, { "basename": "rds4656-sup-0008-tab08.txt", "url": "https://authors.library.caltech.edu/records/z0v9w-c7d75/files/rds4656-sup-0008-tab08.txt" }, { "basename": "rds4656-sup-0009-tab09.txt", "url": "https://authors.library.caltech.edu/records/z0v9w-c7d75/files/rds4656-sup-0009-tab09.txt" }, { "basename": "rds4656-sup-0010-tab10.txt", "url": "https://authors.library.caltech.edu/records/z0v9w-c7d75/files/rds4656-sup-0010-tab10.txt" }, { "basename": "rds4656.pdf", "url": "https://authors.library.caltech.edu/records/z0v9w-c7d75/files/rds4656.pdf" }, { "basename": "rds4656-sup-0001-tab01.txt", "url": "https://authors.library.caltech.edu/records/z0v9w-c7d75/files/rds4656-sup-0001-tab01.txt" }, { "basename": "rds4656-sup-0003-tab03.txt", "url": "https://authors.library.caltech.edu/records/z0v9w-c7d75/files/rds4656-sup-0003-tab03.txt" }, { "basename": "rds4656-sup-0004-tab04.txt", "url": "https://authors.library.caltech.edu/records/z0v9w-c7d75/files/rds4656-sup-0004-tab04.txt" } ], "resource_type": "article", "pub_year": "2002", "author_list": "Bruno, Oscar P.; Sei, Alain; et el." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/ts3s9-wc219", "eprint_id": 90621, "eprint_status": "archive", "datestamp": "2023-08-19 09:36:12", "lastmod": "2023-10-19 14:38:18", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar P." }, "orcid": "0000-0001-8369-3014" } ] }, "title": "Fast, high-order, high-frequency \"accurate Fourier methods\" for scattering problems", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2002 IEEE. \n\nEffort sponsored by the AFOSR under grant numbers F49620-96-1-0008 and F49620-99-1-0010.\n\nPublished - 01018185.pdf
", "abstract": "We present a new set of algorithms and methodologies for the numerical solution of problems of scattering by complex bodies in three-dimensional space. These methods, which are\nbased on integral equations, high-order integration, fast Fourier transforms and highly accurate high-frequency\nmethods, can be used in the solution of problems of electromagnetic and acoustic scattering by surfaces and penetrable scatterers - even in cases in which the scatterers contain geometric singularities such as corners and edges. In all cases the solvers exhibit high-order convergence, they run on low memories and reduced operation counts, and they result in solutions with a high degree of accuracy.", "date": "2002-06", "date_type": "published", "publisher": "IEEE", "place_of_pub": "Piscataway, NJ", "pagerange": "180-183", "id_number": "CaltechAUTHORS:20181102-145356744", "isbn": "0-7803-7330-8", "book_title": "IEEE Antennas and Propagation Society International Symposium", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20181102-145356744", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "F49620-96-1-0008" }, { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "F49620-99-1-0010" } ] }, "doi": "10.1109/APS.2002.1018185", "primary_object": { "basename": "01018185.pdf", "url": "https://authors.library.caltech.edu/records/ts3s9-wc219/files/01018185.pdf" }, "resource_type": "book_section", "pub_year": "2002", "author_list": "Bruno, Oscar P." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/x53ar-ne343", "eprint_id": 90677, "eprint_status": "archive", "datestamp": "2023-08-21 22:47:51", "lastmod": "2023-10-19 14:45:54", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar" }, "orcid": "0000-0001-8369-3014" }, { "id": "Vaynblat-D", "name": { "family": "Vaynblat", "given": "Dimitri" } } ] }, "title": "Shock\u2013induced martensitic phase transitions: critical stresses, Riemann problems and applications", "ispublished": "pub", "full_text_status": "restricted", "keywords": "martensitic phase transitions; shocks; Riemann problems", "note": "\u00a9 2001 The Royal Society. \n\nReceived 2 June 2000; revised 4 December 2000 and 12 March 2001; accepted 29 March 2001. \n\nThe authors acknowledge the support of the DOE through contract W-7405-ENG-48. O.B. gratefully acknowledges support from the NSF, under contract nos DMS-9523292 and DMS-9816802, and the Air Force Office of Scientific Research, Air Force Materials Command, USAF, under grant nos F49620-96-1-0008, F49620-99-1-0010 and F49620-99-1-0193. The US Government is authorized to reproduce and distribute reprints for governmental purposes notwithstanding any copyright notation thereon. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of the Air Force Office of Scientific Research or the US Government.", "abstract": "In this paper we develop a theory for phase transitions in solids under shock loading. This theory applies, in particular, to a class of experiments which, as a result of solid\u2013to\u2013solid phase transitions, give rise to certain characteristic patterns consisting of two shock\u2013like waves. We show that the single assumption that stresses in a phase cannot lie beyond its transition boundaries leads to a complete model for the physical systems at hand. This model is different from others proposed in the literature: it does not make use of kinetic relations and it accounts for the observed wave histories without parameter fitting. The first part of this paper focuses on the basic mathematical description of our model and it presents solutions to the complete set of Riemann problems which could arise as a result of dynamic interactions, including the basic two\u2013wave structures mentioned above. In the second part of the paper we use our Riemann solver to construct general solutions for the piecewise constant initial\u2013value problems usually arising in experiment, and we specialize our solutions to two widely studied polymorphic phase changes: the graphite\u2013diamond transition and the \u03b1\u2013\u2208 transition in iron. We show that, in the presence of well\u2013accepted quations of state for the pure phases, our model leads to close quantitative agreement with a wide range of experimental results; possible sources of disagreement in certain fine features are also discussed. Interestingly, in some cases our theory predicts sequences of events which differ from those generally accepted. In particular, our model predicts a variety of regimes for the iron experiments which previous theoretical investigations had not surmised, and it indicates the existence of certain unexpected transformation domains in the graphite systems.", "date": "2001-12-08", "date_type": "published", "publication": "Proceedings of the Royal Society A: Mathematical, physical, and engineering sciences", "volume": "457", "number": "2016", "publisher": "Royal Society of London", "pagerange": "2871-2920", "id_number": "CaltechAUTHORS:20181106-145235963", "issn": "1364-5021", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20181106-145235963", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "W-7405-ENG-48" }, { "agency": "NSF", "grant_number": "DMS-9523292" }, { "agency": "NSF", "grant_number": "DMS-9816802" }, { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "F49620-96-1-0008" }, { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "F49620-99-1-0010" }, { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "F49620-99-1-0193" } ] }, "doi": "10.1098/rspa.2001.0829", "resource_type": "article", "pub_year": "2001", "author_list": "Bruno, Oscar and Vaynblat, Dimitri" }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/eavav-qmc81", "eprint_id": 90680, "eprint_status": "archive", "datestamp": "2023-08-21 22:47:59", "lastmod": "2023-10-19 14:46:08", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar P." }, "orcid": "0000-0001-8369-3014" }, { "id": "Kunyansky-L-A", "name": { "family": "Kunyansky", "given": "Leonid A." } } ] }, "title": "Surface scattering in three dimensions: an accelerated high\u2013order solver", "ispublished": "pub", "full_text_status": "restricted", "keywords": "wave scattering; integral equation; fast algorithm; fast Fourier transform; equivalent sources; spherical wave expansion", "note": "\u00a9 2001 The Royal Society. \n\nReceived 2 June 2000; revised 19 August 2000; accepted 16 July 2001. \n\nEffort sponsored by the Air Force Office of Scientific Research, Air Force Materials Command, USAF, under grant numbers F49620-96-1-0008, F49620-99-1-0010. O.P.B. gratefully acknowledges support from NSF (through an NYI award and through contracts DMS-9523292 and DMS-9816802), and from the Powell Research Foundation. The US Government is authorized to reproduce and distribute reprints for governmental purposes notwithstanding any copyright notation thereon. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either\nexpressed or implied, of the Air Force Office of Scientific Research or the US Government.", "abstract": "We present a new algorithm for the numerical solution of problems of acoustic scattering by surfaces in three\u2013dimensional space. This algorithm evaluates scattered fields through fast, high\u2013order, accurate solution of the corresponding boundary integral equation. The high\u2013order accuracy of our solver is achieved through use of partitions of unityI together with analytical resolution of kernel singularities. The acceleration, in turn, results from use of high\u2013order equivalent sourceapproximations, which allow for fast evaluation of non\u2013adjacent interactions by means of the three\u2013dimensional fast Fourier transform (FFT). Our acceleration scheme has dramatically lower memory requirements and yields much higher accuracy than existing FFT\u2013accelerated techniques. The present algorithm computes one matrix\u2013vector multiply in O(N^(6/5)logN) to O(N^(4/3)logN) operations (depending on the geometric characteristics of the scattering surface), it exhibits super\u2013algebraic convergence, and it does not suffer from accuracy breakdowns of any kind. We demonstrate the efficiency of our method through a variety of examples. In particular, we show that the present algorithm can evaluate accurately, on a personal computer, scattering from bodies of acoustical sizes (ka) of several hundreds.", "date": "2001-12-08", "date_type": "published", "publication": "Proceedings of the Royal Society A: Mathematical, physical, and engineering sciences", "volume": "457", "number": "2016", "publisher": "Royal Society of London", "pagerange": "2921-2934", "id_number": "CaltechAUTHORS:20181106-151356250", "issn": "1364-5021", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20181106-151356250", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "F49620-96-1-0008" }, { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "F49620-99-1-0010" }, { "agency": "NSF", "grant_number": "DMS-9523292" }, { "agency": "NSF", "grant_number": "DMS-9816802" }, { "agency": "Charles Lee Powell Foundation" } ] }, "doi": "10.1098/rspa.2001.0882", "resource_type": "article", "pub_year": "2001", "author_list": "Bruno, Oscar P. and Kunyansky, Leonid A." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/m426p-dq147", "eprint_id": 90596, "eprint_status": "archive", "datestamp": "2023-08-21 22:46:00", "lastmod": "2023-10-19 14:37:12", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Borcea-L", "name": { "family": "Borcea", "given": "Liliana" } }, { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar" }, "orcid": "0000-0001-8369-3014" } ] }, "title": "On the magneto-elastic properties of elastomer\u2013ferromagnet composites", "ispublished": "pub", "full_text_status": "restricted", "keywords": "A. Inclusions; B. Elastic; Inhomogeneous material; C. Energy methods; Magneto-rheological", "note": "\u00a9 2001 Elsevier. \n\nReceived 25 May 2000, Revised 15 March 2001, Accepted 7 August 2001, Available online 25 October 2001. \n\nThe work of L. Borcea was partially supported by the National Science Foundation under grant numbers DMS-9627407 and DMS-9971209. O. Bruno's effort was sponsored by the Air Force Office of Scientific Research, Air Force Materials Command, USAF, under grant numbers F49620-96-1-0008, F49620-99-1-0010 and F49620-99-1-0193, from DARPA, and through NSF contracts No. DMS-9523292 and DMS-9816802. The US Government is authorized to reproduce and distribute reprints for governmental purposes notwithstanding any copyright notation thereon. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of the Air Force Office of Scientific Research or the US Government.", "abstract": "We study the macroscopic magneto-mechanical behavior of composite materials consisting of a random, statistically homogeneous distribution of ferromagnetic, rigid inclusions embedded firmly in a non-magnetic elastic matrix. Specifically, for given applied elastic and magnetic fields, we calculate the overall deformation and stress\u2013strain relation for such a composite, correct to second order in the particle volume fraction. Our solution accounts for the fully coupled magneto-elastic interactions; the distribution of magnetization in the composite is calculated from the basic minimum energy principle of magneto-elasticity.", "date": "2001-12", "date_type": "published", "publication": "Journal of the Mechanics and Physics of Solids", "volume": "49", "number": "12", "publisher": "Elsevier", "pagerange": "2877-2919", "id_number": "CaltechAUTHORS:20181101-152904594", "issn": "0022-5096", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20181101-152904594", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-9627407" }, { "agency": "NSF", "grant_number": "DMS-9971209" }, { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "F49620-96-1-0008" }, { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "F49620-99-1-0010" }, { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "F49620-99-1-0193" }, { "agency": "Defense Advanced Research Projects Agency (DARPA)" }, { "agency": "NSF", "grant_number": "DMS-9523292" }, { "agency": "NSF", "grant_number": "DMS-9816802" } ] }, "doi": "10.1016/s0022-5096(01)00108-9", "resource_type": "article", "pub_year": "2001", "author_list": "Borcea, Liliana and Bruno, Oscar" }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/yjn76-e9d48", "eprint_id": 90646, "eprint_status": "archive", "datestamp": "2023-08-21 22:46:08", "lastmod": "2023-10-19 14:42:59", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "O." }, "orcid": "0000-0001-8369-3014" }, { "id": "Vaynblat-D", "name": { "family": "Vaynblat", "given": "D." } } ] }, "title": "Two-wave structures in shock-induced martensitic phase transitions", "ispublished": "pub", "full_text_status": "restricted", "keywords": "Phase transition; Shock; Transformation front; Riemann problem", "note": "\u00a9 2001 Published by Elsevier Ltd.", "abstract": "We consider a class of shock-loading experiments which, as a result of solid-to-solid phase transitions, give rise to certain characteristic patterns consisting of two shock-like waves. We show that the single assumption that stresses in a phase cannot lie beyond the transition boundaries leads to a complete mathematical description of the physical problem at hand. In detail, our model only requires knowledge of well-studied material observables: the equations of state (EOS) for the pure phases and the phase transition boundaries. The model presented here is different from others proposed in the literature: it does not make use of kinetic relations, and it accounts for the observed wave histories without parameter fitting. In presence of well-accepted EOS for the pure phases, our model leads to close quantitative agreement with a wide range of experimental results.", "date": "2001-12", "date_type": "published", "publication": "Mathematical and Computer Modelling", "volume": "34", "number": "12-13", "publisher": "Elsevier", "pagerange": "1261-1271", "id_number": "CaltechAUTHORS:20181105-130419396", "issn": "0895-7177", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20181105-130419396", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "doi": "10.1016/S0895-7177(01)00131-5", "resource_type": "article", "pub_year": "2001", "author_list": "Bruno, O. and Vaynblat, D." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/1mvyg-rrp42", "eprint_id": 90676, "eprint_status": "archive", "datestamp": "2023-08-19 07:57:35", "lastmod": "2023-10-19 14:45:48", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar P." }, "orcid": "0000-0001-8369-3014" }, { "id": "Kunyansky-L-A", "name": { "family": "Kunyansky", "given": "Leonid A." } } ] }, "title": "Fast, high-order solution of surface scattering problems", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2001 IEEE. \n\nEffort sponsored by the AFOSR under grant numbers F49620-96-1-0008 and F49620-99-1-0010.\n\nPublished - 00959784.pdf
", "abstract": "We present a new algorithm for the numerical solution of problems of acoustic scattering by surfaces in three-dimensional space. This algorithm evaluates the scattered field, through fast, high-order solution of the boundary integral equation. The high-order of the solver is achieved through use of partition of unity together with analytical resolution of kernel singularities. The acceleration in turn, results from a novel approach which, based on high-order \"two-face\" equivalent source approximations, reduces the evaluation of far interactions to evaluation of 3-D FFTs. We demonstrate its performance with a variety of numerical results. In particular, we show that the present algorithm can evaluate accurately in a personal computer, scattering from bodies of acoustical sizes of several hundreds.", "date": "2001-07", "date_type": "published", "publisher": "IEEE", "place_of_pub": "Piscataway, NJ", "pagerange": "554-557", "id_number": "CaltechAUTHORS:20181106-144801749", "isbn": "0-7803-7070-8", "book_title": "IEEE Antennas and Propagation Society International Symposium. 2001 Digest. Held in conjunction with: USNC/URSI National Radio Science Meeting", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20181106-144801749", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "F49620-96-1-0008" }, { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "F49620-99-1-0010" } ] }, "doi": "10.1109/APS.2001.959784", "primary_object": { "basename": "00959784.pdf", "url": "https://authors.library.caltech.edu/records/1mvyg-rrp42/files/00959784.pdf" }, "resource_type": "book_section", "pub_year": "2001", "author_list": "Bruno, Oscar P. and Kunyansky, Leonid A." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/m5q0a-s6583", "eprint_id": 90645, "eprint_status": "archive", "datestamp": "2023-08-19 07:57:30", "lastmod": "2023-10-19 14:42:53", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Sei-A", "name": { "family": "Sei", "given": "Alain" } }, { "id": "Caponi-M", "name": { "family": "Caponi", "given": "Maria" } }, { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar" }, "orcid": "0000-0001-8369-3014" } ] }, "title": "Polarization ratios anomalies of 3D rough surface scattering as second order effects", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2001 IEEE. \n\nThe authors gratefully acknowledge support from TRW internal research fund.\n\nPublished - 00960200.pdf
", "abstract": "A detailed analysis of the behaviour of electromagnetic scattering from various corrugated bidimensional surfaces is presented. We show that rigorous electromagnetic computations on two dimensional surfaces can in fact yield HH/VV polarization ratios greater than one, with values consistent with those observed experimentally. We also show that HH/VV ratios greater than one are ubiquitous in the case of surfaces of the form f(x, y)=f_1/(x)+f_2(y), known as crossed gratings in optics. Theoretically and numerically, these surfaces are shown to produce backscattered returns for which the first order Rice/Valenzuela term vanishes for off axis incidence. The second order term becomes dominant and has the property that HH returns exceed VV returns for a significant range of incident angles. Our approach is based on the methods of O.Bruno and F. Reitich (see J. Opt. Soc. A., vol.10, p.2551-62, 1993) which yield accurate results for a large range of values of the surface height. In particular, these methods can be used well beyond the domain of applicability of the first order theory of S.O. Rice (1951). The error in our calculations is guaranteed to be several orders of magnitude smaller than the computed values. The high order expansions provided by these methods are essential to determining the role played by the second order terms as they show that these terms indeed dominate most of the backscattering returns for the surfaces mentioned. Classically, large HH/VV ratios were sought by means of first order approximations on one dimensional sinusoidal profiles. In that case, we show that the first order terms do not vanish and the first order theories predict the behaviour of the backscattered returns, for small values of the height to period ratio. However, in the case of a two dimensional bisinusoidal surface, strong polarization dependent anomalies appear in the scattering returns as a result of the contributions of second order terms since, in that case, the first order contributions vanish.", "date": "2001-07", "date_type": "published", "publisher": "IEEE", "place_of_pub": "Piscataway, NJ", "pagerange": "726-729", "id_number": "CaltechAUTHORS:20181105-123901867", "isbn": "0-7803-7070-8", "book_title": "IEEE Antennas and Propagation Society International Symposium. 2001 Digest. Held in conjunction with: USNC/URSI National Radio Science Meeting", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20181105-123901867", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "TRW" } ] }, "doi": "10.1109/APS.2001.960200", "primary_object": { "basename": "00960200.pdf", "url": "https://authors.library.caltech.edu/records/m5q0a-s6583/files/00960200.pdf" }, "resource_type": "book_section", "pub_year": "2001", "author_list": "Sei, Alain; Caponi, Maria; et el." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/3jp5k-w4480", "eprint_id": 90588, "eprint_status": "archive", "datestamp": "2023-08-19 07:43:04", "lastmod": "2023-10-19 14:36:39", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar P." }, "orcid": "0000-0001-8369-3014" }, { "id": "Kunyansky-L-A", "name": { "family": "Kunyansky", "given": "Leonid A." } } ] }, "title": "A Fast, High-Order Algorithm for the Solution of Surface Scattering Problems: Basic Implementation, Tests, and Applications", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 2001 Academic Press. \n\nReceived 21 September 2000, Revised 18 December 2000. \n\nThis effort is sponsored by the Air Force Office of Scientific Research, Air Force Materials Command, USAF, under Grants F49620-96-1-0008 and F49620-99-1-0010. O.B. gratefully acknowledges support from NSF (through an NYI award and through Contracts DMS-9523292 and DMS-9816802) and from the Powell Research Foundation. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of the Air Force Office of Scientific Research or the U.S. Government. \n\nThe U.S. Government's right to retain a nonexclusive royalty-free license in and to the copyright covering this paper, for governmental purposes, is acknowledged.", "abstract": "We present a new algorithm for the numerical solution of problems of acoustic scattering by surfaces in three-dimensional space. This algorithm evaluates scattered fields through fast, high-order solution of the corresponding boundary integral equation. The high-order accuracy of our solver is achieved through use of partitions of unity together with analytical resolution of kernel singularities. The acceleration, in turn, results from use of a novel approach which, based on high-order \"two-face\" equivalent source approximations, reduces the evaluation of far interactions to evaluation of 3-D fast Fourier transforms (FFTs). This approach is faster and substantially more accurate, and it runs on dramatically smaller memories than other FFT and k-space methods. The present algorithm computes one matrix-vector multiplication in O(N^(6/5)log N) to O (N^(4/3) logN) operations, where N is the number of surface discretization points. The latter estimate applies to smooth surfaces, for which our high-order algorithm provides accurate solutions with small values of N; the former, more favorable count is valid for highly complex surfaces requiring significant amounts of subwavelength sampling. Further, our approach exhibits super-algebraic convergence; it can be applied to smooth and nonsmooth scatterers, and it does not suffer from accuracy breakdowns of any kind. In this paper we introduce the main algorithmic components in our approach, and we demonstrate its performance with a variety of numerical results. In particular, we show that the present algorithm can evaluate accurately in a personal computer scattering from bodies of acoustical sizes of several hundreds.", "date": "2001-05-01", "date_type": "published", "publication": "Journal of Computational Physics", "volume": "169", "number": "1", "publisher": "Elsevier", "pagerange": "80-110", "id_number": "CaltechAUTHORS:20181101-152903866", "issn": "0021-9991", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20181101-152903866", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "F49620-96-1-0008" }, { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "F49620-99-1-0010" }, { "agency": "NSF", "grant_number": "DMS-9523292" }, { "agency": "NSF", "grant_number": "DMS-9816802" }, { "agency": "Charles Lee Powell Foundation" } ] }, "doi": "10.1006/jcph.2001.6714", "resource_type": "article", "pub_year": "2001", "author_list": "Bruno, Oscar P. and Kunyansky, Leonid A." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/6vr78-5zw23", "eprint_id": 90656, "eprint_status": "archive", "datestamp": "2023-08-21 22:03:20", "lastmod": "2023-10-19 14:43:48", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar P." }, "orcid": "0000-0001-8369-3014" }, { "id": "Reitich-F", "name": { "family": "Reitich", "given": "Fernando" } } ] }, "title": "Boundary-variation solution of eigenvalue problems for elliptic operators", "ispublished": "pub", "full_text_status": "restricted", "keywords": "boundary perturbations; eigenvalues and eigenfunctions; elliptic operators; analytic continuation", "note": "\u00a9 2001 Birkh\u00e4user Boston. \n\nReceived August 31, 1999; Revision received December 30, 1999. \n\nOB gratefully acknowledges support from NSF (through an NYI award and through contracts No. DMS-9523292 and DMS-9816802), from the AFOSR (through contracts No. F49620-96-1-0008 and F49620-99-1-0010), and from the Powell Research Foundation. FR gratefully acknowledges support from AFOSR through contract No. F49620-99-1-0193 and from NSF through contracts No. DMS-9622555 and DMS-9971379. \n\nEffort sponsored by the Air Force Office of Scientific Research, Air Force Materials Command, USAF, under grant numbers F49620-96-1-0008, F49620-99-1-0010, and F49620-99-1-0193. The U.S. Government is authorized to reproduce and distribute reprints for governmental purposes notwithstanding any copyright notation thereon, The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of the Air Force Office of Scientific Research or the U.S. Government.", "abstract": "We present an algorithm which, based on certain properties of analytic dependence, constructs boundary perturbation expansions of arbitrary order for eigenfunctions of elliptic PDEs. The resulting Taylor series can be evaluated far outside their radii of convergence\u2014by means of appropriate methods of analytic continuation in the domain of complex perturbation parameters. A difficulty associated with calculation of the Taylor coefficients becomes apparent as one considers the issues raised by multiplicity: domain perturbations may remove existing multiple eigenvalues and criteria must therefore be provided to obtain Taylor series expansions for all branches stemming from a given multiple point. The derivation of our algorithm depends on certain properties of joint analyticity (with respect to spatial variables and perturbations) which had not been established before this work. While our proofs, constructions and numerical examples are given for eigenvalue problems for the Laplacian operator in the plane, other elliptic operators can be treated similarly.", "date": "2001-03", "date_type": "published", "publication": "Journal of Fourier Analysis and Applications", "volume": "7", "number": "2", "publisher": "Springer", "pagerange": "169-187", "id_number": "CaltechAUTHORS:20181106-075027317", "issn": "1069-5869", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20181106-075027317", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-9523292" }, { "agency": "NSF", "grant_number": "DMS-9816802" }, { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "F49620-96-1-0008" }, { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "F49620-99-1-0010" }, { "agency": "Charles Lee Powell Foundation" }, { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "F49620-99-1-0193" }, { "agency": "NSF", "grant_number": "DMS-9622555" }, { "agency": "NSF", "grant_number": "DMS-9971379" } ] }, "doi": "10.1007/BF02510422", "resource_type": "article", "pub_year": "2001", "author_list": "Bruno, Oscar P. and Reitich, Fernando" }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/196pb-vvv90", "eprint_id": 90650, "eprint_status": "archive", "datestamp": "2023-08-19 07:04:48", "lastmod": "2023-10-19 14:43:19", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar P." }, "orcid": "0000-0001-8369-3014" }, { "id": "Reitich-F", "name": { "family": "Reitich", "given": "Fernando" } } ] }, "title": "High-Order Boundary Perturbation Methods", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2001 SIAM.\n\nPublished - 1.9780898717594.ch3.pdf
", "abstract": "Perturbation theory is among the most useful and successful analytical tools in applied mathematics. Countless examples of enlightening perturbation analyses have been performed for a wide variety of models in areas ranging from fluid, solid, and quantum mechanics to chemical kinetics and physiology. The field of electromagnetic and acoustic wave propagation is certainly no exception. Many studies of these processes have been based on perturbative calculations where the role of the variation parameter has been played by the wavelength of radiation, material constants, or geometric characteristics. It is this latter instance of geometric perturbations in problems of wave propagation that we shall review in the present chapter.\n\nUse of geometric perturbation theory is advantageous in the treatment of configurations which, however complex, can be viewed as deviations from simpler ones\u2014those for which solutions are known or can be obtained easily. Many uses of such methods exist, including, among others, applications to optics, oceanic and terrain scattering, SAR imaging and remote sensing, and diffraction from ablated, eroded, or deformed objects; see, e.g., [47, 52, 56, 59, 62]. The analysis of the scattering processes involved in such applications poses challenging computational problems that require resolution of the interplay between highly oscillatory waves and interfaces. In the case of oceanic scattering, for instance, nonlinear water wave interactions and capillarity effects give rise to highly oscillatory modulated wave trains that are responsible for the most substantial portions of the scattering returns [35].", "date": "2001", "date_type": "published", "publisher": "Society for Industrial and Applied Mathematics", "place_of_pub": "Philadelphia, PA", "pagerange": "71-109", "id_number": "CaltechAUTHORS:20181105-144641812", "isbn": "978-0-89871-475-3", "book_title": "Mathematical Modeling in Optical Science", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20181105-144641812", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "contributors": { "items": [ { "id": "Bao-Gang", "name": { "family": "Bao", "given": "Gang" } }, { "id": "Cowsar-L", "name": { "family": "Cowsar", "given": "Lawrence" } }, { "id": "Masters-W", "name": { "family": "Masters", "given": "Wen" } } ] }, "doi": "10.1137/1.9780898717594.ch3", "primary_object": { "basename": "1.9780898717594.ch3.pdf", "url": "https://authors.library.caltech.edu/records/196pb-vvv90/files/1.9780898717594.ch3.pdf" }, "resource_type": "book_section", "pub_year": "2001", "author_list": "Bruno, Oscar P. and Reitich, Fernando" }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/vwej5-26m03", "eprint_id": 977, "eprint_status": "archive", "datestamp": "2023-08-21 21:43:26", "lastmod": "2023-10-13 22:03:46", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar P." }, "orcid": "0000-0001-8369-3014" }, { "id": "Sei-A", "name": { "family": "Sei", "given": "Alain" } } ] }, "title": "A fast high-order solver for EM scattering from complex penetrable bodies: TE case", "ispublished": "pub", "full_text_status": "public", "keywords": "Electromagnetic (EM) scattering, iterative methods, nonhomogenous media", "note": "\u00a9 2000 IEEE. \"Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.\" \n\nManuscript received October 5, 1999; revised June 26, 2000. \n\nThis work was supported by the Air Force Office of Scientific Research, Air Force Materials Command, USAF under Grant F49620-96-1-0008. The work of O. P. Bruno was supported by NSF under Contracts DMS-9523292 and the Air Force Office of Scientific Research, Air Force Materials Command, USAF under Grant F49620-99-1-0010 and F49620-99-1-0193.\n\nPublished - BRUieeetap00.pdf
", "abstract": "We present a new high-order integral algorithm for the solution of scattering problems by heterogeneous bodies under TE radiation. Here, a scatterer is represented by a (continuously or discontinuously) varying refractive index n(x) within a two-dimensional (2-D) bounded region. Solutions of the associated Helmholtz equation under given incident fields are then obtained by high-order inversion of the Lippmann-Schwinger integral equation. The algorithm runs in O(N log(N)) operations, where N is the number of discretization points. Our method provides highly accurate solutions in short computing times, even for problems in which the scattering bodies contain complex geometric singularities.", "date": "2000-12", "date_type": "published", "publication": "IEEE Transactions on Antennas and Propagation", "volume": "48", "number": "12", "publisher": "IEEE", "pagerange": "1862-1864", "id_number": "CaltechAUTHORS:BRUieeetap00", "issn": "0018-926X", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:BRUieeetap00", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "F49620-96-1-0008" }, { "agency": "NSF", "grant_number": "DMS-9523292" }, { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "F49620-99-1-0010" }, { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "F49620-99-1-0193" } ] }, "doi": "10.1109/8.901275", "primary_object": { "basename": "BRUieeetap00.pdf", "url": "https://authors.library.caltech.edu/records/vwej5-26m03/files/BRUieeetap00.pdf" }, "resource_type": "article", "pub_year": "2000", "author_list": "Bruno, Oscar P. and Sei, Alain" }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/d3kzw-zqt04", "eprint_id": 90622, "eprint_status": "archive", "datestamp": "2023-08-19 06:02:08", "lastmod": "2023-10-19 14:38:20", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar P." }, "orcid": "0000-0001-8369-3014" }, { "id": "Kunyansky-L-A", "name": { "family": "Kunyansky", "given": "Leonid A." } } ] }, "title": "Fast, high-order solution of surface scattering problems", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2000 IEEE.\n\nPublished - 00874851.pdf
", "abstract": "We present a fast, high-order algorithm for the solution of problems of acoustic scattering from smooth surfaces in three dimensions. The present algorithm computes scattered fields in", "date": "2000-07", "date_type": "published", "publisher": "IEEE", "place_of_pub": "Piscataway, NJ", "pagerange": "1860-1863", "id_number": "CaltechAUTHORS:20181102-151802755", "isbn": "0-7803-6369-8", "book_title": "IEEE Antennas and Propagation Society International Symposium. Transmitting Waves of Progress to the Next Millennium. 2000 Digest. Held in conjunction with: USNC/URSI National Radio Science Meeting", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20181102-151802755", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "doi": "10.1109/APS.2000.874851", "primary_object": { "basename": "00874851.pdf", "url": "https://authors.library.caltech.edu/records/d3kzw-zqt04/files/00874851.pdf" }, "resource_type": "book_section", "pub_year": "2000", "author_list": "Bruno, Oscar P. and Kunyansky, Leonid A." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/7tmtr-v4c20", "eprint_id": 90618, "eprint_status": "archive", "datestamp": "2023-08-21 21:16:18", "lastmod": "2023-10-19 14:38:01", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar P." }, "orcid": "0000-0001-8369-3014" }, { "id": "Goldsztein-G-H", "name": { "family": "Goldsztein", "given": "Guillermo H." } } ] }, "title": "Numerical simulation of martensitic transformations in two- and three-dimensional polycrystals", "ispublished": "pub", "full_text_status": "restricted", "keywords": "Polycrystal; Martensite; Phase transitions; Homogenization; Plasticity", "note": "\u00a9 2000 Elsevier. \n\nReceived 19 January 1999, Revised 16 July 1999, Available online 6 April 2000. \n\nThe authors gratefully acknowledge support from the NSF through Contract No. DMS-9523292. OB gratefully acknowledges support from NSF (through an NYI award and through Contracts DMS-9816802), from the AFOSR (through contracts No. F49620-96-1-0008 and F49620-99-1-0010) and from the Powell Research Foundation. Effort sponsored by the Air Force Office of Scientific Research, Air Force Materials Command, USAF, under grants number F49620-96-1-0008 and F49620-99-1-0010. The US Government is authorized to reproduce and distribute reprints for governmental purposes notwithstanding any copyright notation thereon. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of the Air Force Office of Scientific Research or the US Government.", "abstract": "We introduce a fast numerical method for the evaluation of the effective elastic energy in martensitic polycrystals in two and three dimensions. The overall complexity of the method is O(N) operations, where N is the number of component crystallites. Upper and lower bounds on the energy are also presented which allow us to estimate the accuracy of the numerical results. Our new three-dimensional computations and bounds for random polycrystals, which are the first ones available in the literature, provide substantial insights on the behavior of polycrystalline martensites. They suggest that recoverable strains can be much larger than those attainable with zero energy.", "date": "2000-06-01", "date_type": "published", "publication": "Journal of the Mechanics and Physics of Solids", "volume": "48", "number": "6-7", "publisher": "Elsevier", "pagerange": "1175-1201", "id_number": "CaltechAUTHORS:20181102-135535088", "issn": "0022-5096", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20181102-135535088", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-9523292" }, { "agency": "NSF", "grant_number": "DMS-9816802" }, { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "F49620-96-1-0008" }, { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "F49620-99-1-0010" }, { "agency": "Charles Lee Powell Foundation" } ] }, "doi": "10.1016/s0022-5096(99)00074-5", "resource_type": "article", "pub_year": "2000", "author_list": "Bruno, Oscar P. and Goldsztein, Guillermo H." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/m6k32-s2067", "eprint_id": 90658, "eprint_status": "archive", "datestamp": "2023-08-22 14:13:54", "lastmod": "2023-10-19 14:44:05", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar P." }, "orcid": "0000-0001-8369-3014" }, { "id": "Goldsztein-G-H", "name": { "family": "Goldsztein", "given": "Guillermo H." } } ] }, "title": "A fast algorithm for the simulation of polycrystalline misfits: martensitic transformations in two space dimensions", "ispublished": "pub", "full_text_status": "restricted", "keywords": "polycrystals; nonlinear homogenization; martensitic transformations; elasticity; numerical methods", "note": "\u00a9 1999 The Royal Society. \n\nReceived 4 December 1998; accepted 7 April 1999; Published 8 December 1999. \n\nWe gratefully acknowledge support from NSF (through an NYI award and through contract nos DMS-9523292 and DMS-9816802). O.P.B. gratefully acknowledges support from the AFOSR (through contract nos F49620-96-1-0008 and F49620-99-1-0010) and from the Powell Foundation.", "abstract": "We present a fast method for the solution of problems of elasticity involving microscopic misfit strains. While the main case we consider is that associated with martensitic transformations in polycrystals, our methods can be applied to a variety of systems whose constituents undergo misfit deformations, including polycrystalline magnetostriction, thermal expansion, etc., as well as mathematically analogous phenomena in ferroelectricity and ferromagnetism. The basic component of our method is an explicit solution for Eshelby\u2013type problems on square elements. Fast computation of the polycrystal energy results through a rapidly convergent sequence of approximations which can, in fact, be interpreted as a generalization of a class of upper bounds introduced recently. The overall complexity of the method is O(N) operations, where N is the number of component crystallites. We also present a new lower bound for the energy, giving additional insights on the microscopic phenomena leading to the observed structural behaviour. The present work applies to two\u2013dimensional polycrystals; extensions to the three\u2013dimensional case have been implemented and will be presented elsewhere.", "date": "1999-12-08", "date_type": "published", "publication": "Proceedings of the Royal Society A: Mathematical, physical, and engineering sciences", "volume": "455", "number": "1992", "publisher": "Royal Society of London", "pagerange": "4245-4276", "id_number": "CaltechAUTHORS:20181106-084731697", "issn": "1364-5021", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20181106-084731697", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-9523292" }, { "agency": "NSF", "grant_number": "DMS-9816802" }, { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "F49620-96-1-0008" }, { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "F49620-99-1-0010" }, { "agency": "Charles Lee Powell Foundation" } ] }, "doi": "10.1098/rspa.1999.0500", "resource_type": "article", "pub_year": "1999", "author_list": "Bruno, Oscar P. and Goldsztein, Guillermo H." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/zqd8t-mxc39", "eprint_id": 98234, "eprint_status": "archive", "datestamp": "2023-08-22 13:25:49", "lastmod": "2024-01-14 21:54:42", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "O. P." }, "orcid": "0000-0001-8369-3014" } ] }, "title": "Shape Deforming Phase Transition in Solids: Energetics and pseudoelasticity", "ispublished": "unpub", "full_text_status": "restricted", "keywords": "Martensitic Transformation; Elastic Energy; Habit Plane; Transformation Strain; Free Boundary Condition", "note": "\u00a9 Kluwer Academic Publishers 1999.", "abstract": "Martensitic transformations are shape-deforming phase transitions which can be induced in certain alloys as a result of changes in the imposed strains, stresses or temperatures. The interest in these alloys, which undergo a shape-deforming phase transition from a high temperature phase (austenite) to a low temperature phase (martensite), stems in part from their applicability as elements in active structures. In the present text we outline three recent theories concerning the energy transfers that accompany and determine the martensitic phase change. In \u00a71 we will thus mention the pseudoelastic hysteresis in shape-memory wires and the corresponding treatment of (Leo et al .,1993; Bruno et al .,1995). In \u00a72 we will present some aspects of the discussion of (Bruno et al. ,1996) on equilibrium configurations in polycrystalline martensites. In \u00a73 finally we will describe a computation (Bruno, 1997) which explains typical microstructural lengthscales observed in single-crystalline martensites as resulting from an interplay between elastic energies and dissipative mechanisms.", "date": "1999", "date_type": "published", "publisher": "Kluwer Academic Publishers", "place_of_pub": "Dordrecht", "pagerange": "319-324", "id_number": "CaltechAUTHORS:20190826-124739605", "isbn": "0792352653", "book_title": "IUTAM Symposium on Micro- and Macrostructural Aspects of Thermoplasticity", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190826-124739605", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "contributors": { "items": [ { "id": "Bruhns-O-T", "name": { "family": "Bruhns", "given": "O. T." } }, { "id": "Stein-E", "name": { "family": "Stein", "given": "E." } } ] }, "doi": "10.1007/0-306-46936-7_30", "resource_type": "book_section", "pub_year": "1999", "author_list": "Bruno, O. P." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/zdjrq-j7g26", "eprint_id": 90681, "eprint_status": "archive", "datestamp": "2023-08-19 02:16:19", "lastmod": "2024-01-14 21:09:07", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar P." }, "orcid": "0000-0001-8369-3014" }, { "id": "Reitich-F", "name": { "family": "Reitich", "given": "Fernando" } } ] }, "title": "Bounds on the Effective Elastic Properties of Martensitic Polycrystals", "ispublished": "unpub", "full_text_status": "restricted", "note": "\u00a9 1998 Springer Science+Business Media New York. \n\nOB gratefully acknowledges support from NSF (through an NYI award and through contracts No. DMS-9200002 and DMS-9523292), from the Sloan Foundation (through the fellowships program), from the AFOSR (contract No. F49620-96-1-0008) and from the Powell Research Foundation. FR gratefully acknowledges support from AFOSR through grant No. F49620-95-1-0113 and from NSF through grant No. DMS-9622555.", "abstract": "We draw attention to the problem of estimation of elastic energies in martensitic polycrystals. In particular we introduce a tensorial parameter \u03b7=\u03b7_(ijkl) which contains information about the microgeometry and disorder of the polycrystalline structure. Under the assumption of isotropic elasticity and mild hypothesis on the statistics of the polycrystal, this parameter allows for explicit calculation of rigorous and stringent upper bounds on the effective energy. For circular grains in two dimensions \u03b7 gives the elastic energy resulting from transformation of a single circular inclusion in an elastic matrix and the bounds coincide with those derived recently by Bruno, Reitich and Leo. Consideration of such particular cases shows that our bounds can yield substantial improvements over those obtained under Taylor's constant strain hypothesis. For arbitrary microgeometries the statistical parameter \u03b7 can be calculated by means of two-point correlations functions.", "date": "1998", "date_type": "published", "publisher": "Springer", "place_of_pub": "New York, NY", "pagerange": "51-62", "id_number": "CaltechAUTHORS:20181106-152204596", "isbn": "978-1-4612-7256-4", "book_title": "Mathematics of Multiscale Materials", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20181106-152204596", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-9200002" }, { "agency": "NSF", "grant_number": "DMS-9523292" }, { "agency": "Alfred P. Sloan Foundation" }, { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "F49620-96-1-0008" }, { "agency": "Charles Lee Powell Foundation" }, { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "F49620-95-1-0113" }, { "agency": "NSF", "grant_number": "DMS-9622555" } ] }, "contributors": { "items": [ { "id": "Golden-K-M", "name": { "family": "Golden", "given": "Kenneth M." } }, { "id": "Grimmett-G-R", "name": { "family": "Grimmett", "given": "Geoffrey R." } }, { "id": "James-R-D", "name": { "family": "James", "given": "Richard D." } }, { "id": "Milton-G-W", "name": { "family": "Milton", "given": "Graeme W." } }, { "id": "Sen-P-N", "name": { "family": "Sen", "given": "Pabitra N." } } ] }, "doi": "10.1007/978-1-4612-1728-2_4", "resource_type": "book_section", "pub_year": "1998", "author_list": "Bruno, Oscar P. and Reitich, Fernando" }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/7tcq0-1br03", "eprint_id": 103828, "eprint_status": "archive", "datestamp": "2023-08-22 12:28:49", "lastmod": "2024-01-15 04:31:44", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "O. P." }, "orcid": "0000-0001-8369-3014" } ] }, "title": "Energetics in Martensites", "ispublished": "unpub", "full_text_status": "restricted", "keywords": "Habit Plane; Transformation Strain; Antiplane Shear; Triangular Region; NiTi Wire", "note": "\u00a9 1998 Kluwer Academic Publishers.", "abstract": "Martensitic transformations are shape-deforming phase transitions which can be induced in certain alloys as a result of changes in the imposed strains, stresses or temperatures. The interest in these alloys, which undergo a shape-deforming phase transition from a high temperature phase (austenite) to a low temperature phase (martensite), stems in part from their applicability as elements in active structures. In this paper we focus on the energy transfers that accompany the martensitic phase change. We discuss, in three concrete examples, the ways in which temperature, together with the elastic and dissipated energies, determine the equilibria as well as the quasi-static dynamics in martensites. Thus, in \u00a71 we consider the pseudoelastic hysteresis in shape-memory wires; our treatment draws from (Leo et al., 1993; Bruno et al, 1995). In \u00a72 on the other hand, we follow (Bruno et al., 1996) and discuss equilibrium configurations in polycrystalline martensitic polycrystals. In \u00a73 finally, we present some new theoretical computations for certain typical microstructural lengthscales, the twin widths, observed in single-crystalline martensite twinning.", "date": "1998", "date_type": "published", "publisher": "Kluwer Academic Publishers", "place_of_pub": "Dordrecht", "pagerange": "91-108", "id_number": "CaltechAUTHORS:20200610-144648854", "isbn": "978-0-7923-5122-1", "book_title": "IUTAM Symposium on Transformation Problems in Composite and Active Materials", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20200610-144648854", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "contributors": { "items": [ { "id": "Bahei-El-Din-Y-A", "name": { "family": "Bahei-El-Din", "given": "Yehia A." } }, { "id": "Dvorak-G-J", "name": { "family": "Dvorak", "given": "George J." } } ] }, "doi": "10.1007/0-306-46935-9_7", "resource_type": "book_section", "pub_year": "1998", "author_list": "Bruno, O. P." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/v4zep-cr862", "eprint_id": 90644, "eprint_status": "archive", "datestamp": "2023-08-19 01:30:06", "lastmod": "2024-01-14 21:08:57", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar P." }, "orcid": "0000-0001-8369-3014" } ] }, "title": "Energetics in martensites", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 1997 Society of Photo-Optical Instrumentation Engineers (SPIE).\n\nPublished - 14.pdf
", "abstract": "Martensitic transformations are shape-deforming phase transitions which can be induced in certain alloys as a result of changes in the imposed strains, stresses or temperatures. The interest in these alloys, which undergo a shape-deforming phase transition form a high temperature phase to a low temperature phase, stems in part from their applicability as elements in active structures. In this paper we focus on the energy transfers that accompany the martensitic phase change. We discuss, in three concrete examples, the ways in which temperature, together with the elastic and dissipated energies, determine the equilibria as well as the quasi-static dynamics in martensites. Thus, in \u00a71 we consider the pseudoelastic hysteresis in shape- memory wires; our treatment draws from (7, 3). In \u00a72, on the other hand, we follow and discuss equilibrium configurations in polycrystalline martensitic polycrystals. In \u00a73, finally, we present some new theoretical computations for certain typical microstructural lengthscales, the twin widths, observed in single- crystalline martensite twinning.", "date": "1997-06-13", "date_type": "published", "publisher": "Society of Photo-optical Instrumentation Engineers (SPIE)", "place_of_pub": "Bellingham, WA", "pagerange": "14-24", "id_number": "CaltechAUTHORS:20181105-111232917", "isbn": "9780819424525", "book_title": "Smart Structures and Materials 1997: Mathematics and Control in Smart Structures", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20181105-111232917", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "contributors": { "items": [ { "id": "Varadan-V-V", "name": { "family": "Varadan", "given": "Vasundara V." } }, { "id": "Chandra-J", "name": { "family": "Chandra", "given": "Jagdish" } } ] }, "doi": "10.1117/12.276557", "primary_object": { "basename": "14.pdf", "url": "https://authors.library.caltech.edu/records/v4zep-cr862/files/14.pdf" }, "resource_type": "book_section", "pub_year": "1997", "author_list": "Bruno, Oscar P." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/hv51p-nyg34", "eprint_id": 90682, "eprint_status": "archive", "datestamp": "2023-08-19 00:04:52", "lastmod": "2023-10-19 14:46:20", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar P." }, "orcid": "0000-0001-8369-3014" }, { "id": "Laurence-P", "name": { "family": "Laurence", "given": "Peter" } } ] }, "title": "Existence of three-dimensional toroidal MHD equilibria with nonconstant pressure", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 1996 John Wiley & Sons, Inc. \n\nReceived June 1995. \n\nWe thank the anonymous reviewer for a number of useful suggestions. OB gratefully acknowledges stimulating conversations with P. Garabedian on nonaxisymmetric plasma equilibria; he also wishes to acknowledge support from NSF (through an NYI award and Grants Nos. DMS-9200002 and DMS-9523292), from the Sloan Foundation (through the fellowship program), from the Powell Research Foundation, and from the AFOSR (contract no. F49620-96-1-0008). PL thanks Luigi Chierchia and Rafael de la Llave for valuable discussions concerning KAM theory.", "abstract": "We establish an existence result for the three\u2010dimensional MHD equations (\u2207 x B) x B = \u2207p, \u2207\u00b7B = 0, B\u00b7n|\u2202T = 0 with p \u2260 const in tori T without symmetry. More precisely, our theorems insure the existence of sharp boundary solutions for tori whose departure from axisymmetry is sufficiently small; they allow for solutions to be constructed with an arbitrary number of pressure jumps.", "date": "1996-07", "date_type": "published", "publication": "Communications on Pure and Applied Mathematics", "volume": "49", "number": "7", "publisher": "Wiley", "pagerange": "717-764", "id_number": "CaltechAUTHORS:20181106-153720174", "issn": "0010-3640", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20181106-153720174", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-9200002" }, { "agency": "NSF", "grant_number": "DMS-9523292" }, { "agency": "Alfred P. Sloan Foundation" }, { "agency": "Charles Lee Powell Foundation" }, { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "F49620-96-1-0008" } ] }, "doi": "10.1002/(SICI)1097-0312(199607)49:7<717::AID-CPA3>3.0.CO;2-C", "resource_type": "article", "pub_year": "1996", "author_list": "Bruno, Oscar P. and Laurence, Peter" }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/zayxf-n6z20", "eprint_id": 90586, "eprint_status": "archive", "datestamp": "2023-08-19 00:04:45", "lastmod": "2023-10-19 14:36:29", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar P." }, "orcid": "0000-0001-8369-3014" }, { "id": "Reitich-F", "name": { "family": "Reitich", "given": "Fernando" } }, { "id": "Leo-P-H", "name": { "family": "Leo", "given": "Perry H." } } ] }, "title": "The overall elastic energy of polycrystalline martensitic solids", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 1996 Published by Elsevier. \n\nReceived 24 October 1995. \n\nO.B. gratefully acknowledges support from NSF (through an NYI award and through grants No. DMS-9200002 and DMS-9523292), from the Sloan Foundation (through the fellowships program) from the Powell Research Foundation and from the AFOSR (contract No. F49620-96-1-0008). F.R. gratefully acknowledges support from AFOSR through grant No. F49620-95-1-0113. P.H.L. gratefully acknowledges support from NSF through grant CMS-9503393.", "abstract": "We are concerned with the overall elastic energy in martensitic polycrystals. These are polycrystals whose constituent crystallites can undergo shape-deforming phase transitions as a result of changes in their stress or temperature. We approach the problem of calculation of the nonlinear overall energy via a statistical optimization method which involves solution of a sequence of linear elasticity problems. As a case study we consider simulations on a two-dimensional model in which circular randomly-oriented crystallites are arranged in a square pattern within an elastic matrix. The performance of our present code suggests that this approach can be used to compute the overall energies in realistic three-dimensional polycrystals containing grains of arbitrary shape. \n\nIn addition to numerical results we present upper bounds on the overall energy. Some of these bounds apply to the square array mentioned above. Others apply to polycrystals containing circular, randomly-oriented crystallites with sizes ranging to infinitesimal, and no intergrain matrix. The square-array bounds are consistent with our numerical results. In some regimes they approximate them closely, thus providing an insight on the convergence of the numerical method. On the other hand, in the case of the random array the bounds carry substantial practical significance, since in this case the energy contains no artificial contributions from an elastic matrix. In all the cases we have considered our bounds compare favorably with those obtained under the well-known Taylor hypothesis; they show that, as far as polycrystalline martensite is concerned, calculations of the elastic energy based on the Taylor assumption may lead to substantial overestimates of this quantity.", "date": "1996-07", "date_type": "published", "publication": "Journal of the Mechanics and Physics of Solids", "volume": "44", "number": "7", "publisher": "Elsevier", "pagerange": "1051-1101", "id_number": "CaltechAUTHORS:20181101-152903698", "issn": "0022-5096", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20181101-152903698", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-9200002" }, { "agency": "NSF", "grant_number": "DMS-9523292" }, { "agency": "Alfred P. Sloan Foundation" }, { "agency": "Charles Lee Powell Foundation" }, { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "F49620-96-1-0008" }, { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "F49620-95-1-0113" }, { "agency": "NSF", "grant_number": "CMS-9503393" } ] }, "doi": "10.1016/0022-5096(96)00031-2", "resource_type": "article", "pub_year": "1996", "author_list": "Bruno, Oscar P.; Reitich, Fernando; et el." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/6phrt-96r93", "eprint_id": 90648, "eprint_status": "archive", "datestamp": "2023-08-20 04:48:13", "lastmod": "2023-10-19 14:43:09", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar P." }, "orcid": "0000-0001-8369-3014" }, { "id": "Reitich-F", "name": { "family": "Reitich", "given": "Fernando" } } ] }, "title": "Maxwell equations in a nonlinear Kerr medium", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 1994 The Royal Society. \n\nReceived August 16, 1993; Accepted April 12, 1994. \n\nO.B. gratefully acknowledges support from NSF through grant no. DMS-9200002. This work was partly supported by the Army Research Office and the National Science Foundation through the Center for Nonlinear Analysis.", "abstract": "In this paper we present an exact calculation of the transfer function associated with the nonlinear Fabry\u2013Perot resonator. While our exact result cannot be evaluated in terms of elementary functions, it does permit us to obtain a number of simple approximate expressions of various orders of accuracy. In addition, our derivation yields criteria of validity for the approximate formulae. Our approach is to be compared with others in which approximations are introduced in the model itself, either through the equations or through the boundary conditions. Our lowest order approximate formula turns out to be identical, interestingly, with the result obtained from the slowly varying envelope approximation (SVEA). Thus, our validity criteria apply to the SVEA result, and predict well its domain of validity and its breakdown for short wavelengths and for very high intensities and nonlinearities. The simple higher order formulae we present provide improved estimations in such regimes.", "date": "1994-10-08", "date_type": "published", "publication": "Proceedings of the Royal Society A: Mathematical, physical, and engineering sciences", "volume": "447", "number": "1929", "publisher": "Royal Society of London", "pagerange": "65-76", "id_number": "CaltechAUTHORS:20181105-132848389", "issn": "1364-5021", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20181105-132848389", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-9200002" }, { "agency": "Army Research Office (ARO)" } ] }, "doi": "10.1098/rspa.1994.0129", "resource_type": "article", "pub_year": "1994", "author_list": "Bruno, Oscar P. and Reitich, Fernando" }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/5hpfs-x0k81", "eprint_id": 90657, "eprint_status": "archive", "datestamp": "2023-08-20 04:27:06", "lastmod": "2023-10-19 14:43:55", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar P." }, "orcid": "0000-0001-8369-3014" }, { "id": "Reitich-F", "name": { "family": "Reitich", "given": "Fernando" } } ] }, "title": "Approximation of analytic functions: a method of enhanced convergence", "ispublished": "pub", "full_text_status": "restricted", "keywords": "Power series, enhanced convergence, Pad\u00e9 approximation, conditioning", "note": "\u00a9 1994 American Mathematical Society. \n\nReceived by the editor August 5, 1992 and, in revised form, August 30, 1993. \n\nWe thank the reviewer and Professor W. Gautschi for their valuable comments. The first author gratefully acknowledges support from NSF through grant No. DMS-9200002. This work was partially supported by the Army Research Office and the National Science Foundation through the Center for Nonlinear Analysis.", "abstract": "We deal with a method of enhanced convergence for the approximation of analytic functions. This method introduces conformal transformations in the approximation problems, in order to help extract the values of a given analytic function from its Taylor expansion around a point. An instance of this method, based on the Euler transform, has long been known; recently we introduced more general versions of it in connection with certain problems in wave scattering. In \u00a72 we present a general discussion of this approach.\n\nAs is known in the case of the Euler transform, conformal transformations can enlarge the region of convergence of power series and can enhance substantially the convergence rates inside the circles of convergence. We show that conformal maps can also produce a rather dramatic improvement in the conditioning of Pad\u00e9 approximation. This improvement, which we discuss theoretically for Stieltjes-type functions, is most notorious in cases of very poorly conditioned Pad\u00e9 problems. In many instances, an application of enhanced convergence in conjunction with Pad\u00e9 approximation leads to results which are many orders of magnitude more accurate than those obtained by either classical Pad\u00e9 approximants or the summation of a truncated enhanced series.", "date": "1994-07", "date_type": "published", "publication": "Mathematics of Computation", "volume": "63", "number": "207", "publisher": "American Mathematical Society", "pagerange": "195-213", "id_number": "CaltechAUTHORS:20181106-080649656", "issn": "0025-5718", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20181106-080649656", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-9200002" }, { "agency": "Army Research Office (ARO)" } ] }, "doi": "10.1090/S0025-5718-1994-1240654-9", "resource_type": "article", "pub_year": "1994", "author_list": "Bruno, Oscar P. and Reitich, Fernando" }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/xy92g-fh531", "eprint_id": 90683, "eprint_status": "archive", "datestamp": "2023-08-20 03:24:09", "lastmod": "2023-10-19 14:46:28", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar P." }, "orcid": "0000-0001-8369-3014" }, { "id": "Leo-P-H", "name": { "family": "Leo", "given": "Perry H." } } ] }, "title": "On the stiffness of materials containing a disordered array of microscopic holes or hard inclusions", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 1993 Springer-Verlag. \n\nReceived May 29, 1992. \n\nLeo has been partially supported by the U.S. Army Research Office under grant DA/DAAL03-89-G-0081.", "abstract": "We study the macroscopic mechanical behavior of materials with microscopic holes or hard inclusions. Specifically, we deal with the effective elastic moduli of composites whose microgeometry consists of either soft or hard isolated inclusions surrounded by an elastic matrix. We approach this problem by taking the stiffness of the inclusion phase to be a complex variable, which we eventually evaluate at the soft or hard limits. Our main result states that there is a certain class of non-physical, negative-definite values of the elastic moduli of the inclusion phase for which the effective tensor does not have infinities or become otherwise singular.\n\nWe present applications of this result to the estimation of effective moduli and to homogenization theorems. The first application involves using complexanalytic methods to obtain rigorous and accurate bounds on the effective moduli of the high-contrast composites under consideration. We also discuss the variational estimates of Rubenfeld & Keller, which yield a complementary set of bounds on these moduli. The best bounds are given by a combination of the analytical and variational results. As a second application, we show that certain known theorems of homogenization for materials with holes are simple consequences of our main result, and in this connection we establish corresponding new theorems for materials with hard inclusions. While our rederivation of the homogenization theorems for materials with holes can be closely related to other known constructions, it appears that certain elements provided by our main result are essential in the proof of homogenization for the hard-inclusion case.", "date": "1993-12", "date_type": "published", "publication": "Archive for Rational Mechanics and Analysis", "volume": "121", "number": "4", "publisher": "Springer", "pagerange": "303-338", "id_number": "CaltechAUTHORS:20181106-154533730", "issn": "0003-9527", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20181106-154533730", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Army Research Office (ARO)", "grant_number": "DA/DAAL03-89-G-0081" } ] }, "doi": "10.1007/BF00375624", "resource_type": "article", "pub_year": "1993", "author_list": "Bruno, Oscar P. and Leo, Perry H." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/xy3db-bsn38", "eprint_id": 29660, "eprint_status": "archive", "datestamp": "2023-08-20 02:52:27", "lastmod": "2023-10-24 22:21:39", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar" }, "orcid": "0000-0001-8369-3014" }, { "id": "Friedman-Avner", "name": { "family": "Friedman", "given": "Avner" } }, { "id": "Reitich-F", "name": { "family": "Reitich", "given": "Fernando" } } ] }, "title": "Asymptotic Behavior for a Coalescence Problem", "ispublished": "pub", "full_text_status": "public", "keywords": "Particles, collision, coalescence, asymptotic behavior.", "note": "\u00a9 1993 American Mathematical Society. Received by the editors March 7, 1991. We would like to thank David Ross from Eastman Kodak for suggesting the problem studied in this paper and for several useful conversations. The first author is partially supported by ARO Contract DAAL-03-88-K-0110; the second author is partially supported by National Science Foundation Grant DMS-86-12880; the third author is supported by N.I.S.T. Grant No. DOC/60NANBOD1027.\n\nPublished - BRUtams93.pdf
", "abstract": "Consider spherical particles of volume x having paint on a fraction y of their surface area. The particles are assumed to be homogeneously distributed at each time t, so that one can introduce the density number n (x, y, t). When collision between two particles occurs, the particles will coalesce if and only if they happen to touch each other, at impact, at points which do not belong to the painted portions of their surfaces. Introducing a dynamics for this model, we study the evolution of n (x, y, t) and, in particular, the asymptotic behavior of the mass x n (x, y, t) dx as t \u2192 \u221e.", "date": "1993-07", "date_type": "published", "publication": "Transactions of the American Mathematical Society", "volume": "338", "number": "1", "publisher": "American Mathematical Society", "pagerange": "133-158", "id_number": "CaltechAUTHORS:20120309-093931707", "issn": "0002-9947", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20120309-093931707", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Army Research Office (ARO)", "grant_number": "DAAL-03-88-K-0110" }, { "agency": "NSF", "grant_number": "DMS-86-12880" }, { "agency": "NIST", "grant_number": "DOC/60NANBOD1027" } ] }, "doi": "10.2307/2154448", "primary_object": { "basename": "BRUtams93.pdf", "url": "https://authors.library.caltech.edu/records/xy3db-bsn38/files/BRUtams93.pdf" }, "resource_type": "article", "pub_year": "1993", "author_list": "Bruno, Oscar; Friedman, Avner; et el." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/9j29f-k9s09", "eprint_id": 90641, "eprint_status": "archive", "datestamp": "2023-08-20 00:52:45", "lastmod": "2023-10-19 14:42:44", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar P." }, "orcid": "0000-0001-8369-3014" }, { "id": "Reitich-F", "name": { "family": "Reitich", "given": "Fernando" } } ] }, "title": "Solution of a boundary value problem for the Helmholtz equation via variation of the boundary into the complex domain", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1992 Royal Society of Edinburgh.", "abstract": "In this paper we deal with the problem of diffraction of electromagnetic waves by a periodic interface between two materials. This corresponds to a two-dimensional quasi-periodic boundary value problem for the Helmholtz equation. We prove that solutions behave analytically with respect to variations of the interface. The interest of this result is both theoretical \u2013 the legitimacy of power series expansions in the parameters of the problem has indeed been questioned \u2013 and, perhaps more importantly, practical: we have found that the solution can be computed on the basis of this observation. The simple algorithm that results from such boundary variations is described. To establish the property of analyticity of the solution for the grating f_\u03c3(x) = \u03b4f(x) with respect to the height \u03b4, we present a holomorphic formulation of the problem using surface potentials. We show that the densities entering into the potential theoretic formulation are analytic with respect to variations of the boundary, or, in other words, that the integral operator that results from the transmission conditions at the interface is invertible in a space of holomorphic functions of the variables (x, y, \u03b4). This permits us to conclude, in particular, that the partial derivatives of u with respect to \u03b4 at \u03b4 = 0 satisfy certain boundary value problems for the Helmholtz equation, in regions with plane boundaries, which can be solved in a closed form.", "date": "1992", "date_type": "published", "publication": "Proceedings of the Royal Society of Edinburgh: Section A Mathematics", "volume": "122", "number": "3-4", "publisher": "Royal Society of Edinburgh", "pagerange": "317-340", "id_number": "CaltechAUTHORS:20181105-103653124", "issn": "0308-2105", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20181105-103653124", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "doi": "10.1017/S0308210500021132", "resource_type": "article", "pub_year": "1992", "author_list": "Bruno, Oscar P. and Reitich, Fernando" }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/g55hk-ymg67", "eprint_id": 90678, "eprint_status": "archive", "datestamp": "2023-08-20 00:03:15", "lastmod": "2023-10-19 14:45:58", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar P." }, "orcid": "0000-0001-8369-3014" } ] }, "title": "The effective conductivity of strongly heterogeneous composites", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 1991 The Royal Society. \n\nReceived 1 October 1990; accepted 20 November 1990. \n\nWe thank Professors D. Kinderlehrer, R. Kohn, G. Milton and S. Torquato for stimulating conversations on the subject of this paper. Support from ARO under contract DAAL-03-88-K-0110 is also gratefully acknowledged.", "abstract": "We deal with the effective conductivity m = m(z) of two phase, ordered or disordered mixtures consisting of particles of material of conductivity z inserted in a matrix of conductivity 1. We focus on finding bounds on the set of values of z for which the function m is singular or vanishes, and we apply our results to the estimation of the effective conductivity of high contrast mixtures (z = 0 or z = \u221e). We find that the zeroes and singularities of the function m lie on an interval of the negative real axis, which depends on the shape of the particles and the interparticle distances. Our results agree with previous numerical calculations for periodic arrays of spheres. In some cases we show that our estimates are optimal. We apply our results about the zeroes and singularities together with the complex variable method, and find bounds on the effective conductivity of matrix-particle random composites. These bounds give good estimations even in cases of high contrast, and, in many cases, they improve substantially over the bounds obtained by other methods, for the same types of high contrast mixtures.", "date": "1991-05-08", "date_type": "published", "publication": "Proceedings of the Royal Society A: Mathematical, physical, and engineering sciences", "volume": "433", "number": "1888", "publisher": "Royal Society of London", "pagerange": "353-381", "id_number": "CaltechAUTHORS:20181106-145800580", "issn": "1364-5021", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20181106-145800580", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Army Research Office (ARO)", "grant_number": "DAAL-03-88-K-0110" } ] }, "doi": "10.1098/rspa.1991.0053", "resource_type": "article", "pub_year": "1991", "author_list": "Bruno, Oscar P." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/8dk8c-2wc40", "eprint_id": 90642, "eprint_status": "archive", "datestamp": "2023-08-19 23:32:38", "lastmod": "2023-10-19 14:42:47", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar P." }, "orcid": "0000-0001-8369-3014" } ] }, "title": "Taylor expansions and bounds for the effective conductivity and the effective elastic moduli of multicomponent composites and polycrystals", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1991 IOS Press, Inc. \n\nReceived 4 April 1990.", "abstract": "We describe a construction, based on variational inequalities, which gives a hierarchy of upper and lower bounds (of odd orders 2k+1), on the various effective moduli of random multiphase materials and polycrystals. The bounds of order 2k+1 on a given effective modulus can be explicitly evaluated if a truncated Taylor expansion of the given modulus is known to order 2k+1. Our approach is motivated by prior investigations of Beran and other authors. Our calculations do not involve Green functions or n-point correlation functions, and they are very simple. We thus rederive known and obtain new sequences of bounds on the different effective moduli. We also describe a method that, for cell materials (i.e. materials in which cells of smaller and smaller length scales cover all space, with material properties assigned at random), permits one to calculate the truncated Taylor expansions that are needed for the explicit evaluation of the bounds. In connection with this, we show that the first coefficient in the low volume fraction expansion of any effective modulus of a cell material, coincides with the corresponding low volume fraction coefficient for an array of cells randomly distributed in a matrix.", "date": "1991", "date_type": "published", "publication": "Asymptotic Analysis", "volume": "4", "number": "4", "publisher": "IOS Press", "pagerange": "339-365", "id_number": "CaltechAUTHORS:20181105-104502314", "issn": "0921-7134", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20181105-104502314", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "doi": "10.3233/ASY-1991-4404", "resource_type": "article", "pub_year": "1991", "author_list": "Bruno, Oscar P." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/b51bg-yk259", "eprint_id": 90686, "eprint_status": "archive", "datestamp": "2023-08-22 07:46:17", "lastmod": "2023-10-19 14:46:45", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "O." }, "orcid": "0000-0001-8369-3014" }, { "id": "Golden-K", "name": { "family": "Golden", "given": "K." } } ] }, "title": "Interchangeability and bounds on the effective conductivity of the square lattice", "ispublished": "pub", "full_text_status": "restricted", "keywords": "Effective conductivity; random resistor network; composites; cell materials; perturbation expansions; bounds", "note": "\u00a9 1990 Plenum Publishing Corporation. \n\nReceived July 13, 1989; final May 11, 1990. \n\nThe work of O.B. was supported in part by ARO through grant DAAL 03-88-F-0110, and the work of K.G. by AFOSR through grant AFOSR-90-0203.", "abstract": "The effective conductivity \u03c3* of an infinitely interchangeable two-component random medium is considered. This class of media includes cell materials in the continuum and the bond lattice on \u2124^d, where the cells or bonds are randomly assigned the conductivities \u03c3_1 and \u03c3_2 (\u03c3_1, \u03c3_2 ne0) with probabilities p_1 and p_2 = 1\u2212p_1. A rigorous basis for the very old and widely used low volume fraction expansion of \u03c3* is established, by proving that \u03c3* is an analytic function of p_2 in a suitable domain containing [0, 1]. In the case of the bond lattice in d = 2, rigorous fourth-order upper and lower bounds on \u03c3* valid for all p_2, \u03c3_1, and \u03c3_2 are derived. The four perturbation coefficients entering into the bounds are obtained from the first-order volume fraction coefficient using the method of infinite interchangeability.", "date": "1990-10", "date_type": "published", "publication": "Journal of Statistical Physics", "volume": "61", "number": "1-2", "publisher": "Springer", "pagerange": "365-386", "id_number": "CaltechAUTHORS:20181107-080002180", "issn": "0022-4715", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20181107-080002180", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Army Research Office (ARO)", "grant_number": "DAAL 03-88-F-0110" }, { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "AFOSR-90-0203" } ] }, "doi": "10.1007/BF01013970", "resource_type": "article", "pub_year": "1990", "author_list": "Bruno, O. and Golden, K." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/cp693-yh590", "eprint_id": 90647, "eprint_status": "archive", "datestamp": "2023-08-19 23:04:16", "lastmod": "2023-10-19 14:43:02", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar P." }, "orcid": "0000-0001-8369-3014" } ] }, "title": "The effective conductivity of an infinitely interchangeable mixture", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1990 Wiley Periodicals, Inc. \n\nManuscript received: 01 July 1989.", "abstract": "We are concerned with the estimation of the effective electrical conductivity of random heterogenous materials. The purpose of this paper is to discuss a property of \"statistical symmetry\" verified by the symmetric cell materials of Miller. This property will be referred to as infinite interchangeability. \n\nThe usual way to approach cell materials is through n\u2010point correlation functions. The property of infinite interchangebility permits us to approach cell materials from a completely different point of view. Our main result is a simple algorithm, based on this symmetry property, for computing any coefficient of the perturbation expansion in terms of information from the dilute limit. Specifically, knowledge of the coefficients of the expansion in powers of the volume fraction up to order r allows for computation of the perturbation expansion coefficients up to order (2r + 1). This result, which was previously known for r = 2 in the isotropic case and for r = 1 in the anisotropic case, can also be obtained from the standard correlation function approach, as pointed out by Milton.", "date": "1990-09", "date_type": "published", "publication": "Communications on Pure and Applied Mathematics", "volume": "43", "number": "6", "publisher": "Wiley", "pagerange": "769-807", "id_number": "CaltechAUTHORS:20181105-131823303", "issn": "0010-3640", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20181105-131823303", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "doi": "10.1002/cpa.3160430604", "resource_type": "article", "pub_year": "1990", "author_list": "Bruno, Oscar P." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/pcfyy-8jt32", "eprint_id": 9059, "eprint_status": "archive", "datestamp": "2023-08-22 07:42:07", "lastmod": "2023-10-16 21:53:35", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Avellaneda-M", "name": { "family": "Avellaneda", "given": "Marco" } }, { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar" }, "orcid": "0000-0001-8369-3014" } ] }, "title": "Effective conductivity and average polarizability of random polycrystals", "ispublished": "pub", "full_text_status": "public", "keywords": "POLYCRYSTALS; RANDOMNESS; THERMAL CONDUCTIVITY; SERIES EXPANSION; TENSORS; ANISOTROPY; POLARIZABILITY; VECTORS; CRYSTAL ORIENTATION; DISTRIBUTION; NUMERICAL DATA; CORRELATION FUNCTIONS; CALCULATION METHODS; SYMMETRY", "note": "\u00a9 1990 American Institute of Physics. \n\nReceived 2 October 1989; accepted 28 March 1990.\n\nWe are grateful to Professor G. Milton and Dr. J. Berryman for useful discussion which helped improve this paper. \n\nThis research was partially supported by a National Science Foundation Grant No. NSF-DMS-8802739 and by the US Army Research Office through Grant Nos. ARO-DAAL-0389K0039 and ARO-DAAL-0388K0110.\n\nPublished - ALLjmp90.pdf
", "abstract": "A third-order expansion for the effective thermal conductivity tensor \u03ba* of anisotropic polycrystalline cell materials is derived. The coefficients of the expansion are given in terms of the average polarizability tensor, a nondimensional quantity determined from the grain shape and crystallographic orientation distributions independent of other details of the microgeometry such as two (or more) particle correlation functions. Explicit numerical results for a wide variety of microgeometries made of ellipsoidal cells are obtained. This calculation uses a new method that exploits the symmetry properties of the effective conductivity tensor of a cell material as a function of the single-crystal conductivities.", "date": "1990-08", "date_type": "published", "publication": "Journal of Mathematical Physics", "volume": "31", "number": "8", "publisher": "American Institute of Physics", "pagerange": "2047-2056", "id_number": "CaltechAUTHORS:AVEjmp90", "issn": "0022-2488", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:AVEjmp90", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-8802739" }, { "agency": "Army Research Office (ARO)", "grant_number": "DAAL-0389K0039" }, { "agency": "Army Research Office (ARO)", "grant_number": "DAAL-0388K0110" } ] }, "doi": "10.1063/1.528656", "primary_object": { "basename": "ALLjmp90.pdf", "url": "https://authors.library.caltech.edu/records/pcfyy-8jt32/files/ALLjmp90.pdf" }, "resource_type": "article", "pub_year": "1990", "author_list": "Avellaneda, Marco and Bruno, Oscar" }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/1d1b8-1ba67", "eprint_id": 90590, "eprint_status": "archive", "datestamp": "2023-08-19 20:48:36", "lastmod": "2023-10-19 14:36:46", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar P." }, "orcid": "0000-0001-8369-3014" } ] }, "title": "Three problems concerning ideals of differentiable functions", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 1988 Published by Elsevier. Under an Elsevier user license. \n\nCommunicated by F. W. Lawvere. \n\nReceived 29 December 1986. \n\nResearch partially supported by the \"Groupe Interuniversitaire en Etudes Categoriques\". \n\nWe thank Gonzalo Reyes and van Qu\u00ea for suggesting the problems and for their encouragement.", "abstract": "In this paper, we study the validity of the following two statements in the internal logic of the toposes of Synthetic Differential Geometry:\n1. (1) The integral of f is non-negative if f is non-negative; \n\n2. (2) If f=0 in the set of non-negative reals, and f=0 in the set of non-negative reals, then f=0. We find statements (1) and (2) to be true in the toposes considered. We also prove that \n\n3. (3) For n greater than two, the arrow tn from the line to itself is not a stable effective epic. This answers a question raised by Qu\u00ea-Moerdijk-Reyes.", "date": "1988-08", "date_type": "published", "publication": "Journal of Pure and Applied Algebra", "volume": "53", "number": "1-2", "publisher": "Elsevier", "pagerange": "15-32", "id_number": "CaltechAUTHORS:20181101-152904050", "issn": "0022-4049", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20181101-152904050", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Groupe Interuniversitaire en Etudes Categoriques" } ] }, "doi": "10.1016/0022-4049(88)90009-6", "resource_type": "article", "pub_year": "1988", "author_list": "Bruno, Oscar P." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/xs9nm-b7568", "eprint_id": 90591, "eprint_status": "archive", "datestamp": "2023-08-19 19:12:23", "lastmod": "2023-10-19 14:36:55", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar P." }, "orcid": "0000-0001-8369-3014" } ] }, "title": "Vector fields on R^R in well adapted models of synthetic differential geometry", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 1987 Published by Elsevier. Under an Elsevier user license. \n\nReceived 21 February 1985. \n\nCommunicated by F.W. Lawvere.", "abstract": "Vector fields in infinite-dimensional manifolds play an important role in differential topology-geometry. In particular the case when the manifolds are C\u221e-map spaces. The well developed theory modeled in Banach spaces does not apply here. Instead a theory modeled in Frechet spaces is being considered. This is a theory which seems to be a much less straightforward generalization of the finite-dimensional case. The well adapted models of S.D.G. lead naturally to treat these spaces. We investigate here the case of the 'manifold' R^R, whose space of global sections is C^\u221e(\u211d). We prove that to integrate a vector field in R^R is equivalent to a certain differential problem in C^\u221e(\u211d). To do this, we previously characterize the maps R^R \u2192 R^R, R^R X R^R in the topos by means of the functions they induce in the respective spaces of global sections.", "date": "1987", "date_type": "published", "publication": "Journal of Pure and Applied Algebra", "volume": "45", "number": "1", "publisher": "Elsevier", "pagerange": "1-14", "id_number": "CaltechAUTHORS:20181101-152904132", "issn": "0022-4049", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20181101-152904132", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "doi": "10.1016/0022-4049(87)90080-6", "resource_type": "article", "pub_year": "1987", "author_list": "Bruno, Oscar P." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/71rgw-m5q40", "eprint_id": 90685, "eprint_status": "archive", "datestamp": "2023-08-19 18:33:07", "lastmod": "2023-10-19 14:46:35", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar P." }, "orcid": "0000-0001-8369-3014" } ] }, "title": "On a property of ideals of differentiable functions", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 1986 Australian Mathematical Society. \n\nReceived 16 July 1985.", "abstract": "Let J \u2286 C^\u221e(R^n) be any ideal. Since a function of the variables t = (t_1,...,t_n) is a function of the variables (t,x) = (t_1,...,t_n,x_1,...x_p) which does not depend on x, we have J \u2286 C^\u221e(R^(n+p)). Of course, J is not an ideal of C^\u221e(R^(n+p), but it generates an ideal that we call J(t,x). Consider the following statement (1) on J: \"Given any f \u03f5 C^\u221e (R^(n+p), f \u03f5 J(t,x) if and only if for every fixed a \u03f5 R^p, f(t,a) \u03f5 J\".\n\nIn this paper we show that statement (1) holds for a large class of finitely generated ideals although not for all of them. We say that ideals satisfying statement (1) have line determined extensions. We characterize these ideals to be closed ideals J(t) (in the sense of Whitney) such that for all p \u2208 \u2115, the ideal J(t,x) is also closed. Finally, some non-trivial examples are developed.", "date": "1986-04", "date_type": "published", "publication": "Bulletin of the Australian Mathematical Society", "volume": "33", "number": "2", "publisher": "Cambridge University Press", "pagerange": "293-305", "id_number": "CaltechAUTHORS:20181106-160538496", "issn": "0004-9727", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20181106-160538496", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "doi": "10.1017/S0004972700003166", "resource_type": "article", "pub_year": "1986", "author_list": "Bruno, Oscar P." }, { "id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/29fcb-rk043", "eprint_id": 90687, "eprint_status": "archive", "datestamp": "2023-08-19 17:28:59", "lastmod": "2023-10-19 14:46:48", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bruno-O-P", "name": { "family": "Bruno", "given": "Oscar P." }, "orcid": "0000-0001-8369-3014" } ] }, "title": "Logical opens of exponential objects", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1985 Andr\u00e9e C. Ehresmann et les auterus.\n\nPublished - CTGDC_1985__26_3_311_0.pdf
", "abstract": "Let X = C^\u221e(R^p)/J, Y = C^\u221e(R^n)/I be two representable objects in the Dubuc topos D (see Secsion 0) where J has line determined extensions (0.3). The main result in this paper (Theorem 1.11) says that the global section functor \u0393 establishes a bijection between Penon open sub-objects of Y^x and open subsets of \u0393(Y^x) in the C^\u221e-CO topology. We show also that when I = {0}, we can assume J arbitrary (1.12). However, the restriction on J (of having line determined extensions) is seen to be unavoidable in general.\nWe precede the article with a Section 0 where we recall all these notions and fix the notations.", "date": "1985", "date_type": "published", "publication": "Cahiers de Topologie et G\u00e9om\u00e9trie Diff\u00e9rentielle Cat\u00e9goriques", "volume": "26", "number": "3", "publisher": "Amiens", "pagerange": "311-323", "id_number": "CaltechAUTHORS:20181107-080545986", "issn": "1245-530X", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20181107-080545986", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "primary_object": { "basename": "CTGDC_1985__26_3_311_0.pdf", "url": "https://authors.library.caltech.edu/records/29fcb-rk043/files/CTGDC_1985__26_3_311_0.pdf" }, "resource_type": "article", "pub_year": "1985", "author_list": "Bruno, Oscar P." } ]