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Part II: the N-Dimensional Case", author = "Hou, Thomas Y. and Zhang, Shumao", journal = "arXiv", month = "December", year = "2022", url = "https://resolver.caltech.edu/CaltechAUTHORS:20230227-194427740", } @article {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/119521, title ="Exponentially Convergent Multiscale Finite Element Method", author = "Chen, Yifan and Hou, Thomas Y. and Wang, Yixuan", journal = "arXiv", month = "December", year = "2022", url = "https://resolver.caltech.edu/CaltechAUTHORS:20230227-194420642", } @article {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/118564, title ="Fourier Continuation for Exact Derivative Computation in Physics-Informed Neural Operators", author = "Maust, Haydn and Li, Zongyi and Wang, Yixuan and Leibovici, Daniel and Bruno, Oscar and Hou, Thomas and Anandkumar, Anima", journal = "arXiv", month = "November", year = "2022", url = "https://resolver.caltech.edu/CaltechAUTHORS:20221221-004750416", } @article {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/119517, title ="Stable nearly self-similar blowup of the 2D Boussinesq and 3D Euler equations with smooth data", author = "Chen, Jiajie and Hou, Thomas Y.", journal = "arXiv", month = "October", year = "2022", url = "https://resolver.caltech.edu/CaltechAUTHORS:20230227-191437852", } @article {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/117078, title ="Potential Singularity of the 3D Euler Equations in the Interior Domain", author = "Hou, Thomas Y.", journal = "Foundations of Computational Mathematics", month = "September", year = "2022", doi = "https://doi.org/10.1007/s10208-022-09585-5", url = "https://resolver.caltech.edu/CaltechAUTHORS:20220919-922490500", } @article {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/117077, title ="Potentially Singular Behavior of the 3D Navier-Stokes Equations", author = "Hou, Thomas Y.", journal = "Foundations of Computational Mathematics", month = "September", year = "2022", doi = "https://doi.org/10.1007/s10208-022-09578-4", url = "https://resolver.caltech.edu/CaltechAUTHORS:20220919-258327700", } @article {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/115058, title ="A potential two-scale traveling wave singularity for 3D incompressible Euler equations", author = "Hou, Thomas Y. and Huang, De", journal = "Physica D", volume = "435", pages = "Art. 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Series A", volume = "41", number = "1", pages = "169-199", month = "January", year = "2021", doi = "https://doi.org/10.3934/dcds.2020296", url = "https://resolver.caltech.edu/CaltechAUTHORS:20200122-075925100", } @article {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/118576, title ="Fast Global Convergence for Low-rank Matrix Recovery via Riemannian Gradient Descent with Random Initialization", author = "Hou, Thomas Y. and Li, Zhenzhen and Zhang, Ziyun", journal = "arXiv", month = "December", year = "2020", url = "https://resolver.caltech.edu/CaltechAUTHORS:20221221-220354531", } @article {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/100909, title ="A prototype knockoff filter for group selection with FDR control", author = "Chen, Jiajie and Hou, Anthony and Hou, Thomas Y.", journal = "Information and Inference", volume = "9", number = "2", pages = "271-288", month = "June", year = "2020", doi = "https://doi.org/10.1093/imaiai/iaz012", url = "https://resolver.caltech.edu/CaltechAUTHORS:20200124-145020991", } @article {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/100875, title ="A Minimal Mechanosensing Model Predicts Keratocyte Evolution on Flexible Substrates", author = "Zhang, Zhiwen and Rosakis, Phoebus and Hou, Thomas Y. and Ravichandran, Guruswami", journal = "Journal of the Royal Society Interface", volume = "17", number = "166", pages = "Art. No. 20200175", month = "May", year = "2020", doi = "https://doi.org/10.1098/rsif.2020.0175", url = "https://resolver.caltech.edu/CaltechAUTHORS:20200123-103312153", } @article {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/100844, title ="Analysis of Asymptotic Escape of Strict Saddle Sets in Manifold Optimization", author = "Hou, Thomas Y. and Li, Zhenzhen and Zhang, Ziyun", journal = "arXiv", month = "November", year = "2019", url = "https://resolver.caltech.edu/CaltechAUTHORS:20200122-133158689", } @article {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/100143, title ="Formation of Finite-Time Singularities in the 3D Axisymmetric Euler Equations: A Numerics Guided Study", author = "Luo, Guo and Hou, Thomas Y.", journal = "SIAM Review", volume = "61", number = "4", pages = "793-835", month = "November", year = "2019", doi = "https://doi.org/10.1137/19m1288061", url = "https://resolver.caltech.edu/CaltechAUTHORS:20191202-133631090", } @article {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/100852, title ="A class of robust numerical methods for solving dynamical systems with multiple time scales", author = "Hou, Thomas Y. and Wang, Zhongjian and Zhang, Zhiwen", journal = "arXiv", month = "September", year = "2019", url = "https://resolver.caltech.edu/CaltechAUTHORS:20200122-143531561", } @article {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/96584, title ="Solving Bayesian inverse problems from the perspective of deep generative networks", author = "Hou, Thomas Y. and Lam, Ka Chun and Zhang, Pengchuan and Zhang, Shumao", journal = "Computational Mechanics", volume = "64", number = "2", pages = "395-408", month = "August", year = "2019", doi = "https://doi.org/10.1007/s00466-019-01739-7", url = "https://resolver.caltech.edu/CaltechAUTHORS:20190620-093003600", } @article {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/97052, title ="A Model Reduction Method for Multiscale Elliptic Pdes with Random Coefficients Using an Optimization Approach", author = "Hou, Thomas Y. and Ma, Dingjiong and Zhang, Zhiwen", journal = "Multiscale Modeling and Simulation", volume = "17", number = "2", pages = "826-853", month = "June", year = "2019", doi = "https://doi.org/10.1137/18m1205844", url = "https://resolver.caltech.edu/CaltechAUTHORS:20190711-100817562", } @article {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/99835, title ="A pseudo knockoff filter for correlated features", author = "Chen, Jiajie and Hou, Anthony and Hou, Thomas Y.", journal = "Information and Inference", volume = "8", number = "2", pages = "313-341", month = "June", year = "2019", doi = "https://doi.org/10.1093/imaiai/iay012", url = "https://resolver.caltech.edu/CaltechAUTHORS:20191114-104110525", } @article {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/94725, title ="A Fast Hierarchically Preconditioned Eigensolver Based on Multiresolution Matrix Decomposition", author = "Hou, Thomas Y. and Huang, De and Lam, Ka Chun and Zhang, Ziyun", journal = "Multiscale Modeling and Simulation", volume = "17", number = "1", pages = "260-306", month = "January", year = "2019", doi = "https://doi.org/10.1137/18m1180827", url = "https://resolver.caltech.edu/CaltechAUTHORS:20190416-073721627", } @article {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/74783, title ="Potential Singularity for a Family of Models of the Axisymmetric Incompressible Flow", author = "Hou, Thomas Y. and Jin, Tianling and Liu, Pengfei", journal = "Journal of Nonlinear Science", volume = "28", number = "6", pages = "2217-2247", month = "December", year = "2018", doi = "https://doi.org/10.1007/s00332-017-9370-9", url = "https://resolver.caltech.edu/CaltechAUTHORS:20170306-105506989", } @article {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/85641, title ="Global regularity for a family of 3D models of the axi-symmetric Navier–Stokes equations", author = "Hou, Thomas Y. and Liu, Pengfei and Wang, Fei", journal = "Nonlinearity", volume = "31", number = "5", pages = "Art. 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"https://resolver.caltech.edu/CaltechAUTHORS:20151023-103928257", } @article {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/65372, title ="Sparse Time-Frequency decomposition for multiple signals with same frequencies", author = "Hou, Thomas Y. and Shi, Zuoqiang", month = "July", year = "2015", url = "https://resolver.caltech.edu/CaltechAUTHORS:20160315-152129723", } @article {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/65368, title ="Self-similar Singularity of a 1D Model for the 3D Axisymmetric Euler Equations", author = "Hou, Thomas Y. and Liu, Pengfei", month = "February", year = "2015", url = "https://resolver.caltech.edu/CaltechAUTHORS:20160315-133921211", } @article {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/57147, title ="A Multiscale Data-Driven Stochastic Method for Elliptic PDEs with Random Coefficients", author = "Zhang, Zhiwen and Ci, Maolin and Hou, Thomas Y.", journal = "Multiscale Modeling and Simulation", volume = "13", number = "1", pages = "173-204", month = "January", year = "2015", doi = "https://doi.org/10.1137/130948136", url = "https://resolver.caltech.edu/CaltechAUTHORS:20150501-105112539", } @article {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/53802, title ="A heterogeneous stochastic FEM framework for elliptic PDEs", author = "Hou, Thomas Y. and Liu, Pengfei", journal = "Journal of Computational Physics", volume = "281", pages = "942-969", month = "January", year = "2015", doi = "https://doi.org/10.1016/j.jcp.2014.10.020", url = "https://resolver.caltech.edu/CaltechAUTHORS:20150115-154548810", } @article {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/57633, title ="Sparse Time Frequency Representations and Dynamical Systems", author = "Hou, Thomas Y. and Shi, Zuoqiang and Tavallali, Peyman", journal = "Communications in Mathematical Sciences", volume = "13", number = "3", pages = "673-694", month = "January", year = "2015", doi = "https://doi.org/10.4310/CMS.2015.v13.n3.a4", url = "https://resolver.caltech.edu/CaltechAUTHORS:20150519-083002339", } @article {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/54284, title ="Extraction of Intrawave Signals Using the Sparse Time-Frequency Representation Method", author = "Tavallali, Peyman and Hou, Thomas Y. and Shi, Zuoqiang", journal = "Multiscale Modeling and Simulation", volume = "12", number = "4", pages = "1458-1493", month = "October", year = "2014", doi = "https://doi.org/10.1137/140957767", url = "https://resolver.caltech.edu/CaltechAUTHORS:20150202-093859868", } @article {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/48880, title ="Potentially singular solutions of the 3D axisymmetric Euler equations", author = "Luo, Guo and Hou, Thomas Y.", journal = "Proceedings of the National Academy of Sciences of the United States of America", volume = "111", number = "36", pages = "12968-12973", month = "September", year = "2014", doi = "https://doi.org/10.1073/pnas.1405238111", url = "https://resolver.caltech.edu/CaltechAUTHORS:20140825-230506377", } @article {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/53563, title ="Adaptive ANOVA-Based Data-Driven Stochastic Method for Elliptic PDEs with Random Coefficient", author = "Zhang, Zhiwen and Hu, Xin and Hou, Thomas Y. and Lin, Guang and Yan, Mike", journal = "Communications in Computational Physics", volume = "16", number = "3", pages = "571-598", month = "September", year = "2014", doi = "https://doi.org/10.4208/cicp.270913.020414a", url = "https://resolver.caltech.edu/CaltechAUTHORS:20150112-104708436", } @article {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/47705, title ="Convergence of a data-driven time–frequency analysis method", author = "Hou, Thomas Y. and Shi, Zuoqiang and Tavallali, Peyman", journal = "Applied and Computational Harmonic Analysis", volume = "37", number = "2", pages = "235-270", month = "September", year = "2014", doi = "https://doi.org/10.1016/j.acha.2013.12.004", url = "https://resolver.caltech.edu/CaltechAUTHORS:20140731-103641810", } @article {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/48854, title ="Intrinsic frequency for a systems approach to haemodynamic waveform analysis with clinical applications", author = "Pahlevan, Niema M. and Tavallali, Peyman and Rinderknecht, Derek and Petrasek, Danny and Matthews, Ray V. and Hou, Thomas Y. and Gharib, Morteza", journal = "Journal of the Royal Society Interface", volume = "11", number = "98", pages = "Art. No. 20140617 ", month = "September", year = "2014", doi = "https://doi.org/10.1098/​rsif.2014.0617 ", url = "https://resolver.caltech.edu/CaltechAUTHORS:20140825-134136758", } @article {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/45116, title ="On Finite Time Singularity and Global Regularity of an Axisymmetric Model for the 3D Euler Equations", author = "Hou, Thomas Y. and Lei, Zhen and Luo, Guo and Wang, Shu and Zou, Chen", journal = "Archive for Rational Mechanics and Analysis", volume = "212", number = "2", pages = "683-706", month = "May", year = "2014", doi = "https://doi.org/10.1007/s00205-013-0717-6", url = "https://resolver.caltech.edu/CaltechAUTHORS:20140422-134241808", } @article {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/54275, title ="Toward the Finite-Time Blowup of the 3D Axisymmetric Euler Equations: A Numerical Investigation", author = "Luo, Guo and Hou, Thomas Y.", journal = "Multiscale Modeling & Simulation", volume = "12", number = "4", pages = "1722-1776", month = "April", year = "2014", doi = "https://doi.org/10.1137/140966411", url = "https://resolver.caltech.edu/CaltechAUTHORS:20150202-082208889", } @article {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/44693, title ="A Multiscale Model Reduction Method for Partial Differential Equations", author = "Ci, Maolin and Hou, Thomas Y. and Shi, Zuoqiang", journal = "ESAIM-Mathematical Modelling and Numerical Analysis", volume = "48", number = "2", pages = "449-474", month = "March", year = "2014", doi = "https://doi.org/10.1051/m2an/2013115", url = "https://resolver.caltech.edu/CaltechAUTHORS:20140407-110251743", } @article {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/43324, title ="Sparse time-frequency representation of nonlinear and nonstationary data", author = "Hou, Thomas Yizhao and Shi, Zuoqiang", journal = "Science China Mathematics", volume = "56", number = "12", pages = "2489-2506", month = "December", year = "2013", doi = "https://doi.org/10.1007/s11425-013-4733-7", url = "https://resolver.caltech.edu/CaltechAUTHORS:20140113-074436396", } @article {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/65369, title ="On the Finite-Time Blowup of a 1D Model for the 3D Incompressible Euler Equations", author = "Hou, Thomas Y. and Luo, Guo", month = "November", year = "2013", url = "https://resolver.caltech.edu/CaltechAUTHORS:20160315-134409579", } @article {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/41036, title ="Generalized multiscale finite element methods (GMsFEM)", author = "Efendiev, Yalchin and Galvis, Juan and Hou, Thomas Y.", journal = "Journal of Computational Physics", volume = "251", pages = "116-135", month = "October", year = "2013", doi = "https://doi.org/10.1016/j.jcp.2013.04.045 ", url = "https://resolver.caltech.edu/CaltechAUTHORS:20130830-131942975", } @article {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/48819, title ="A decadal microwave record of tropical air temperature from AMSU-A/aqua observations", author = "Shi, Yuan and Li, King-Fai and Yung, Yuk L. and Aumann, Hartmut H. and Shi, Zuoqiang and Hou, Thomas Y.", journal = "Climate Dynamics", volume = "41", number = "5-6", pages = "1385-1405", month = "September", year = "2013", doi = "https://doi.org/10.1007/s00382-013-1696-x", url = "https://resolver.caltech.edu/CaltechAUTHORS:20140822-131136037", } @article {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/39587, title ="Data-driven time–frequency analysis", author = "Hou, Thomas Y. and Shi, Zuoqiang", journal = "Applied and Computational Harmonic Analysis", volume = "35", number = "2", pages = "284-308", month = "September", year = "2013", doi = "https://doi.org/10.1016/j.acha.2012.10.001", url = "https://resolver.caltech.edu/CaltechAUTHORS:20130725-100732399", } @article {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/39189, title ="A dynamically bi-orthogonal method for time-dependent\r stochastic partial differential equations I: Derivation and\r algorithms", author = "Cheng, Mulin and Hou, Thomas Y. and Zhang, Zhiwen", journal = "Journal of Computational Physics", volume = "242", pages = "843-868", month = "June", year = "2013", doi = "https://doi.org/10.1016/j.jcp.2013.02.033", url = "https://resolver.caltech.edu/CaltechAUTHORS:20130702-134527463", } @article {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/39174, title ="A dynamically bi-orthogonal method for time-dependent\r stochastic partial differential equations II: Adaptivity and\r generalizations", author = "Cheng, Mulin and Hou, Thomas Y. and Zhang, Zhiwen", journal = "Journal of Computational Physics", volume = "242", pages = "753-776", month = "June", year = "2013", doi = "https://doi.org/10.1016/j.jcp.2013.02.020", url = "https://resolver.caltech.edu/CaltechAUTHORS:20130701-154101667", } @article {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/36167, title ="Multiscale modeling of incompressible turbulent flows", author = "Hou, T. Y. and Hu, X. and Hussain, F.", journal = "Journal of Computational Physics", volume = "232", number = "1", pages = "383-396", month = "January", year = "2013", doi = "https://doi.org/10.1016/j.jcp.2012.08.029", url = "https://resolver.caltech.edu/CaltechAUTHORS:20130104-102700776", } @article {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/37298, title ="Numerical simulation of water resources problems: Models, methods, and trends", author = "Miller, Cass T. and Dawson, Clint N. and Farthing, Matthew W. and Hou, Thomas Y. and Huang, Jingfang and Kees, Christopher E. and Kelley, C. T. and Langtangen, Hans Petter", journal = "Advances in Water Resources", volume = "51", pages = "405-437", month = "January", year = "2013", url = "https://resolver.caltech.edu/CaltechAUTHORS:20130305-095227632", } @article {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/31616, title ="On singularity formation of a 3D model for incompressible Navier–Stokes equations", author = "Hou, Thomas Y. and Shi, Zuoqiang and Wang, Shu", journal = "Advances in Mathematics", volume = "230", number = "2", pages = "607-641", month = "June", year = "2012", doi = "https://doi.org/10.1016/j.aim.2012.02.015", url = "https://resolver.caltech.edu/CaltechAUTHORS:20120523-112912673", } @article {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/29846, title ="Dynamic growth estimates of maximum vorticity for 3D incompressible Euler equations and the SQG model", author = "Hou, Thomas Y. and Shi, Zuoqiang", journal = "Discrete and Continuous Dynamical Systems", volume = "32", number = "5", pages = "1449-1463", month = "May", year = "2012", doi = "https://doi.org/10.3934/dcds.2012.32.1449 ", url = "https://resolver.caltech.edu/CaltechAUTHORS:20120326-132813054", } @book {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/101080, title ="Numerical Analysis of Multiscale Problems", author = "Graham, Ivan G. and Hou, Thomas Y. and Lakkis, Omar and Scheichl, Robert", volume = "83", month = "January", year = "2012", isbn = "978-3-642-22060-9", url = "https://resolver.caltech.edu/CaltechAUTHORS:20200203-134704241", } @article {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/65367, title ="On the Local Well-posedness of a 3D Model for Incompressible Navier-Stokes Equations with Partial Viscosity", author = "Hou, Thomas Y. and Shi, Zuoqiang and Wang, Shu", month = "July", year = "2011", url = "https://resolver.caltech.edu/CaltechAUTHORS:20160315-133702384", } @article {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/29719, title ="Adaptive data analysis via sparse time-frequency representation", author = "Hou, Thomas Y. and Shi, Zuoqiang", journal = "Advances in Adaptive Data Analysis", volume = "3", number = "1-2", pages = "1-28", month = "April", year = "2011", doi = "https://doi.org/10.1142/S1793536911000647", url = "https://resolver.caltech.edu/CaltechAUTHORS:20120314-131024684", } @article {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/89350, title ="Introduction", author = "Hou, Thomas Y. and Tai, Xue-Cheng", journal = "Advances in Adaptive Data Analysis", volume = "3", number = "1-2", pages = "v-vi", month = "April", year = "2011", doi = "https://doi.org/10.1142/S1793536911000672", url = "https://resolver.caltech.edu/CaltechAUTHORS:20180904-093329630", } @article {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/22550, title ="On Singularity Formation of a Nonlinear Nonlocal System", author = "Hou, Thomas Y. and Li, Congming and Shi, Zuoqiang and Wang, Shu and Yu, Xinwei", journal = "Archive for Rational Mechanics and Analysis", volume = "199", number = "1", pages = "117-144", month = "January", year = "2011", doi = "https://doi.org/10.1007/s00205-010-0319-5", url = "https://resolver.caltech.edu/CaltechAUTHORS:20110228-113453092", } @article {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/29801, title ="Introduction", author = "Hou, Thomas Y. and Tai, Xue-Cheng", journal = "Advances in Adaptive Data Analysis", volume = "3", number = "1-2", pages = "v-vi", month = "January", year = "2011", url = "https://resolver.caltech.edu/CaltechAUTHORS:20120322-080850518", } @article {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/20397, title ="A new multiscale finite element method for high-contrast elliptic interface problems", author = "Chu, C.-C. and Graham, I. G. and Hou, T.-Y.", journal = "Mathematics of Computation", volume = "79", number = "272", pages = "1915-1955", month = "October", year = "2010", url = "https://resolver.caltech.edu/CaltechAUTHORS:20101012-100934632", } @book_section {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/88644, title ="Introduction to the Theory of Incompressible Inviscid Flows", author = "Hou, Thomas Y. and Yu, Xinwei", number = "13", pages = "1-71", month = "June", year = "2009", doi = "https://doi.org/10.1142/9789814273282_0001", isbn = "978-981-4273-27-5", url = "https://resolver.caltech.edu/CaltechAUTHORS:20180808-083855888", } @book {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/88643, title ="Multi-Scale Phenomena in Complex Fluids: Modeling, Analysis and Numerical Simulation", author = "Hou, Thomas Y. and Liu, Chun and Liu, Jian-Guo", number = "12", month = "June", year = "2009", isbn = "978-981-4273-25-1", url = "https://resolver.caltech.edu/CaltechAUTHORS:20180808-083034185", } @article {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/14443, title ="On the Partial Regularity of a 3D Model of the Navier-Stokes Equations", author = "Hou, Thomas Y. and Lei, Zhen", journal = "Communications in Mathematical Physics", volume = "287", number = "2", pages = "589-612", month = "April", year = "2009", doi = "https://doi.org/10.1007/s00220-008-0689-9", url = "https://resolver.caltech.edu/CaltechAUTHORS:20090624-105309162", } @article {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/14326, title ="On the stabilizing effect of convection in three-dimensional incompressible flows", author = "Hou, Thomas Y. and Lei, Zhen", journal = "Communications on Pure and Applied Mathematics", volume = "62", number = "4", pages = "501-564", month = "April", year = "2009", doi = "https://doi.org/10.1002/cpa.20254", url = "https://resolver.caltech.edu/CaltechAUTHORS:20090528-090507806", } @article {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/12553, title ="Multiscale analysis for convection dominated transport equations", author = "Hou, Thomas Y. and Liang, Dong", journal = "Discrete and Continuous Dynamical Systems", volume = "23", number = "1-2", pages = "281-298", month = "January", year = "2009", url = "https://resolver.caltech.edu/CaltechAUTHORS:HOUdcds09", } @article {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/23018, title ="Blow-up or no blow-up? A unified computational and analytic approach to 3D incompressible Euler and Navier–Stokes equations ", author = "Hou, Thomas Y.", journal = "Acta Numerica", volume = "18", pages = "277-346", month = "January", year = "2009", url = "https://resolver.caltech.edu/CaltechAUTHORS:20110321-155230291", } @book {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/88755, title ="Multiscale Finite Element Methods: Theory and Applications", author = "Hou, Thomas and Efendiev, Yalchin", volume = "4", month = "January", year = "2009", isbn = "978-0-387-09495-3", url = "https://resolver.caltech.edu/CaltechAUTHORS:20180810-134356708", } @book_section {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/18758, title ="Multiscale computations for flow and transport in porous media", author = "Hou, Thomas Y.", journal = "unknown", number = "12", pages = "175-285", month = "January", year = "2009", isbn = "9789814273268", url = "https://resolver.caltech.edu/CaltechAUTHORS:20100622-112319775", } @article {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/15179, title ="Stable Fourth Order Stream-Function Methods for Incompressible Flows with Boundaries", author = "Hou, Thomas Y. and Wetton, Brian R.", journal = "Journal of Computational Mathematics", volume = "27", number = "4", pages = "441-458", month = "January", year = "2009", url = "https://resolver.caltech.edu/CaltechAUTHORS:20090819-164116745", } @article {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/13788, title ="Removing the Stiffness of Elastic Force from the Immersed Boundary Method for the 2D Stokes Equations", author = "Hou, Thomas Y. and Shi, Zuoqiang", journal = "Journal of Computational Physics", volume = "227", number = "21", pages = "9138-9169", month = "November", year = "2008", doi = "https://doi.org/10.1016/j.jcp.2008.03.002", url = "https://resolver.caltech.edu/CaltechAUTHORS:HOUjcp08b", } @article {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/13608, title ="An efficient semi-implicit immersed boundary method\r for the Navier–Stokes equations", author = "Hou, T. Y. and Shi, Z.", journal = "Journal of Computational Physics", volume = "227", number = "20", pages = "8968-8991", month = "October", year = "2008", url = "https://resolver.caltech.edu/CaltechAUTHORS:HOUjcp08a", } @article {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/16343, title ="Global Regularity of the 3D Axi-symmetric\r Navier-Stokes Equations with Anisotropic Data", author = "Hou, Thomas Y. and Lei, Zhen and Li, Congming", journal = "Communications in Partial Differential Equation", volume = "33", number = "9", pages = "1622-1637", month = "September", year = "2008", doi = "https://doi.org/10.1080/03605300802108057 ", url = "https://resolver.caltech.edu/CaltechAUTHORS:20091014-100827184", } @article {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/11759, title ="Multiscale simulations of porous media flows in flow-based coordinate system", author = "Efendiev, Y. and Hou, T. and Strinopoulos, T.", journal = "Computational Geosciences", volume = "12", number = "3", pages = "257-272", month = "September", year = "2008", doi = "https://doi.org/10.1007/s10596-007-9073-7", url = "https://resolver.caltech.edu/CaltechAUTHORS:EFEcg08", } @article {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/11915, title ="Multiscale finite element methods for stochastic porous media flow equations and application to uncertainty quantification", author = "Dostert, P. and Efendiev, Y. and Hou, T. Y.", journal = "Computer Methods in Applied Mechanics and Engineering", volume = "197", number = "43-44", pages = "3445-3455", month = "August", year = "2008", url = "https://resolver.caltech.edu/CaltechAUTHORS:DOScmame08", } @book_section {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/11984, title ="Multiscale Computations for Flow and Transport in Heterogeneous Media", author = "Efendiev, Yalchin and Hou, Thomas Y.", number = "1946", pages = "169-248", month = "July", year = "2008", doi = "https://doi.org/10.1007/978-3-540-79574-2_4", isbn = "978-3-540-79573-5", url = "https://resolver.caltech.edu/CaltechAUTHORS:EFElnm08", } @article {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/65578, title ="Dynamic stability of the three-dimensional axisymmetric Navier-Stokes equations with swirl", author = "Hou, Thomas Y. and Li, Congming", journal = "Communications on Pure and Applied Mathematics", volume = "61", number = "5", pages = "661-697", month = "May", year = "2008", doi = "https://doi.org/10.1002/cpa.20212", url = "https://resolver.caltech.edu/CaltechAUTHORS:20160322-093035560", } @article {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/10548, title ="Multiscale Analysis and Computation for the Three-Dimensional Incompressible Navier–Stokes Equations", author = "Hou, Thomas Y. and Yang, Danping and Ran, Hongyu", journal = "Multiscale Modeling and Simulation", volume = "6", number = "4", pages = "1317-1346", month = "March", year = "2008", url = "https://resolver.caltech.edu/CaltechAUTHORS:HOUmms08", } @book_section {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/100935, title ="Numerical Study of Nearly Singular Solutions of the 3-D Incompressible Euler Equations", author = "Hou, Thomas Y. and Li, Ruo", number = "3", pages = "39-66", month = "January", year = "2008", doi = "https://doi.org/10.1007/978-3-540-68850-1_3", isbn = "978-3-540-68848-8", url = "https://resolver.caltech.edu/CaltechAUTHORS:20200127-092428769", } @article {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/65572, title ="Computing nearly singular solutions using pseudo-spectral methods", author = "Hou, Thomas Y. and Li, Ruo", journal = "Journal of Computational Physics", volume = "226", number = "1", pages = "379-397", month = "September", year = "2007", doi = "https://doi.org/10.1016/j.jcp.2007.04.014", url = "https://resolver.caltech.edu/CaltechAUTHORS:20160322-083351617", } @article {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/101841, title ="Mathematical modeling and simulation of aquatic and aerial animal locomotion", author = "Hou, T. Y. and Stredie, V. G. and Wu, T. Y.", journal = "Journal of Computational Physics", volume = "225", number = "2", pages = "1603-1631", month = "August", year = "2007", doi = "https://doi.org/10.1016/j.jcp.2007.02.015", url = "https://resolver.caltech.edu/CaltechAUTHORS:20200310-145803950", } @article {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/65576, title ="Nonexistence of locally self-similar blow-up for the 3D incompressible Navier-Stokes equations", author = "Hou, Thomas Y. and Li, Ruo", journal = "Discrete and Continuous Dynamical Systems", volume = "18", number = "4", pages = "637-642", month = "August", year = "2007", doi = "https://doi.org/10.3934/dcds.2007.18.637", url = "https://resolver.caltech.edu/CaltechAUTHORS:20160322-091323469", } @article {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/19675, title ="Multiscale finite element methods for porous media flows and their applications", author = "Efendiev, Y. and Hou, T. Y.", journal = "Applied Numerical Mathematics", volume = "57", number = "5-7", pages = "577-596", month = "May", year = "2007", url = "https://resolver.caltech.edu/CaltechAUTHORS:20100826-114814124", } @article {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/9102, title ="Organized structures, memory, and the decay of turbulence", author = "Hou, Thomas Y.", journal = "Proceedings of the National Academy of Sciences of the United States of America", volume = "104", number = "16", pages = "6498-6499", month = "April", year = "2007", doi = "https://doi.org/10.1073/pnas.0700639104", url = "https://resolver.caltech.edu/CaltechAUTHORS:HOUpnas07", } @article {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/7178, title ="Bridging Atomistic/Continuum Scales in Solids with Moving Dislocations", author = "Tang, Shao-Qiang and Liu, Wing K. and Karpov, Eduard G. and Hou, Thomas Y.", journal = "Chinese Physics Letters", volume = "24", number = "1", pages = "161-164", month = "January", year = "2007", url = "https://resolver.caltech.edu/CaltechAUTHORS:TANcpl07", } @book_section {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/98052, title ="A Relay-Zone Technique for Computing Dynamic Dislocations", author = "Tang, S. Q. and Liu, W. K. and Karpov, E. G. and Hou, T. Y.", pages = "228-228", month = "January", year = "2007", doi = "https://doi.org/10.1007/978-3-540-75999-7_28", isbn = "978-3-540-75998-0", url = "https://resolver.caltech.edu/CaltechAUTHORS:20190820-155926497", } @article {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/7553, title ="A Framework for Modeling Subgrid Effects for Two-Phase Flows in Porous Media", author = "Hou, Thomas Y. and Westhead, Andrew and Yang, Danping", journal = "Multiscale Modeling & Simulation", volume = "5", number = "4", pages = "1087-1127", month = "December", year = "2006", url = "https://resolver.caltech.edu/CaltechAUTHORS:HOUmms06", } @article {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/65575, title ="Dynamic Depletion of Vortex Stretching and Non-Blowup of the 3-D Incompressible Euler Equations", author = "Hou, Thomas Y. and Li, Ruo", journal = "Journal of Nonlinear Science", volume = "16", number = "6", pages = "639-664", month = "December", year = "2006", doi = "https://doi.org/10.1007/s00332-006-0800-3", url = "https://resolver.caltech.edu/CaltechAUTHORS:20160322-090700507", } @article {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/6811, title ="On Global Well-Posedness of the Lagrangian Averaged Euler Equations", author = "Hou, Thomas Y. and Li, Congming", journal = "SIAM Journal on Mathematical Analysis", volume = "38", number = "3", pages = "782-794", month = "August", year = "2006", url = "https://resolver.caltech.edu/CaltechAUTHORS:HOUsiamjma06", } @article {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/65567, title ="Level Set Dynamics and the Non-blowup of the 2D Quasi-geostrophic Equation", author = "Deng, J. and Hou, T. Y. and Li, R. and Yu, X.", month = "April", year = "2006", url = "https://resolver.caltech.edu/CaltechAUTHORS:20160322-071936317", } @article {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/9623, title ="A 3D Numerical Method for Studying Vortex Formation Behind a Moving Plate", author = "Hou, T. Y. and Stredie, V. G. and Wu, T. Y.", journal = "Communications in Computational Physics", volume = "1", number = "2", pages = "207-228", month = "April", year = "2006", url = "https://resolver.caltech.edu/CaltechAUTHORS:HOUccp06", } @article {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/75864, title ="Improved Geometric Conditions for Non-Blowup of the 3D Incompressible Euler Equation", author = "Deng, Jian and Hou, Thomas Y. and Yu, Xinwei", journal = "Communications in Partial Differential Equations", volume = "31", number = "2", pages = "293-306", month = "January", year = "2006", doi = "https://doi.org/10.1080/03605300500358152", url = "https://resolver.caltech.edu/CaltechAUTHORS:20170408-133541409", } @book_section {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/23868, title ="Multiscale computation of isotropic homogeneous turbulent\r flow", author = "Hou, Tom and Yang, Danping and Ran, Hongyu", number = "408", pages = "111-135", month = "January", year = "2006", isbn = "0-8218-3968-3", url = "https://resolver.caltech.edu/CaltechAUTHORS:20110602-094821767", } @article {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/4466, title ="Preconditioning Markov Chain Monte Carlo Simulations Using Coarse-Scale Models", author = "Efendiev, Y. and Hou, T. and Luo, W.", journal = "SIAM Journal on Scientific Computing", volume = "28", number = "2", pages = "776-803", month = "January", year = "2006", url = "https://resolver.caltech.edu/CaltechAUTHORS:EFEsiamjsc06", } @article {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/76154, title ="Multiscale analysis in Lagrangian formulation for the 2-D incompressible Euler equation", author = "Hou, Thomas Y. and Yang, Danping and Ran, Hongyu", journal = "Discrete and Continuous Dynamical Systems", volume = "13", number = "5", pages = "1153-1186", month = "December", year = "2005", doi = "https://doi.org/10.3934/dcds.2005.13.1153", url = "https://resolver.caltech.edu/CaltechAUTHORS:20170408-161459048", } @article {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/85587, title ="Multiscale modelling and computation of fluid flow", author = "Hou, Thomas Y.", journal = "International Journal for Numerical Methods in Fluids", volume = "47", number = "8-9", pages = "707-719", month = "March", year = "2005", doi = "https://doi.org/10.1002/fld.866", url = "https://resolver.caltech.edu/CaltechAUTHORS:20180404-083725024", } @article {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/65571, title ="Geometric Properties and Nonblowup of 3D Incompressible Euler Flow", author = "Deng, Jian and Hou, Thomas Y. and Yu, Xinwei", journal = "Communications in Partial Differential Equations", volume = "30", number = "1-2", pages = "225-243", month = "January", year = "2005", doi = "https://doi.org/10.1081/PDE-200044488", url = "https://resolver.caltech.edu/CaltechAUTHORS:20160322-075428588", } @article {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/27203, title ="A modified particle method for semilinear hyperbolic systems with oscillatory solutions ", author = "Fetecau, R. C. and Hou, T. Y.", journal = "Methods and Applications of Analysis", volume = "11", number = "4", pages = "573-604", month = "December", year = "2004", url = "https://resolver.caltech.edu/CaltechAUTHORS:20111013-071805594", } @article {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/27179, title ="Multiscale Finite Element Methods for Nonlinear Problems and their Applications", author = "Efendiev, Y. and Hou, T. Y. and Ginting, V.", journal = "Communications in Mathematical Sciences", volume = "2", number = "4", pages = "553-589", month = "December", year = "2004", url = "https://resolver.caltech.edu/CaltechAUTHORS:20111012-093928630", } @article {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/27219, title ="Removing the cell resonance error in the multiscale finite element method via a Petrov-Galerkin formulation\r ", author = "Hou, Thomas Y. and Wu, Xiao-Hui and Zhang, Yu", journal = "Communications in Mathematical Sciences", volume = "2", number = "2", pages = "185-205", month = "June", year = "2004", url = "https://resolver.caltech.edu/CaltechAUTHORS:20111014-070953819", } @article {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/24952, title ="Homogenization of incompressible Euler equations", author = "Hou, Thomas Y. and Yang, Dan-ping and Wang, Ke", journal = "Journal of Computational Mathematics", volume = "22", number = "2", pages = "220-229", month = "March", year = "2004", url = "https://resolver.caltech.edu/CaltechAUTHORS:20110819-082640450", } @article {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/3127, title ="Singularity formation in three-dimensional vortex sheets", author = "Hou, Thomas Y. and Hu, Gang and Zhang, Pingwen", journal = "Physics of Fluids", volume = "15", number = "1", pages = "147-172", month = "January", year = "2003", url = "https://resolver.caltech.edu/CaltechAUTHORS:HOUpof03", } @article {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/7271, title ="A mixed multiscale finite element method for elliptic problems with oscillating coefficients", author = "Chen, Zhiming and Hou, Thomas Y.", journal = "Mathematics of Computation", volume = "72", number = "242", pages = "541-576", month = "June", year = "2002", url = "https://resolver.caltech.edu/CaltechAUTHORS:CHEmc03", } @article {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/101478, title ="Multiscale Domain Decomposition Methods for Elliptic Problems with High Aspect Ratios", author = "Aarnes, Jørg and Hou, Thomas Y.", journal = "Acta Mathematicae Applicatae Sinica, English Series", volume = "18", number = "1", pages = "63-76", month = "March", year = "2002", doi = "https://doi.org/10.1007/s102550200004", url = "https://resolver.caltech.edu/CaltechAUTHORS:20200221-160350446", } @book_section {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/101589, title ="Coastal hydrodynamics of ocean waves on beach", author = "Zhang, Jin E. and Wu, Theodore Y. and Hou, Thomas Y.", journal = "Advances in Applied Mechanics", volume = "37", pages = "89-165", month = "January", year = "2001", doi = "https://doi.org/10.1016/s0065-2156(00)80005-8", isbn = "9780120020379", url = "https://resolver.caltech.edu/CaltechAUTHORS:20200226-133732456", } @article {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/1900, title ="The singular perturbation of surface tension in Hele-Shaw flows", author = "Ceniceros, Hector D. and Hou, Thomas Y.", journal = "Journal of Fluid Mechanics", volume = "409", pages = "251-272", month = "April", year = "2000", url = "https://resolver.caltech.edu/CaltechAUTHORS:CENjfm00", } @article {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/856, title ="Convergence of a nonconforming multiscale finite element method", author = "Efendiev, Yalchin R. and Hou, Thomas Y. and Wu, Xiao-Hui", journal = "SIAM Journal on Numerical Analysis", volume = "37", number = "3", pages = "888-910", month = "March", year = "2000", url = "https://resolver.caltech.edu/CaltechAUTHORS:EFEsiam00", } @article {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/1917, title ="Numerical study of Hele-Shaw flow with suction", author = "Ceniceros, Hector D. and Hou, Thomas Y. and Si, Helen", journal = "Physics of Fluids", volume = "11", number = "9", pages = "2471-2486", month = "September", year = "1999", url = "https://resolver.caltech.edu/CaltechAUTHORS:CENpof99", } @article {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/7556, title ="Dynamic generation of capillary waves", author = "Ceniceros, Hector D. and Hou, Thomas Y.", journal = "Physics of Fluids", volume = "11", number = "5", pages = "1042-1050", month = "May", year = "1999", url = "https://resolver.caltech.edu/CaltechAUTHORS:CENpof99a", } @article {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/7554, title ="Effect of finite computational domain on turbulence scaling law in both physical and spectral spaces", author = "Hou, Thomas Y. and Wu, Xiao-Hui and Chen, Shiyi and Zhou, Ye", journal = "Physical Review E", volume = "58", number = "5", pages = "5841-5844", month = "November", year = "1998", url = "https://resolver.caltech.edu/CaltechAUTHORS:HOUpre98", } @article {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/760, title ="Numerical Study of Free Interface Problems Using Boundary Integral Methods", author = "Hou, Thomas Yizhao", journal = "Documenta Mathematica", volume = "Extra ", number = "Volume", pages = "601-610", month = "January", year = "1998", url = "https://resolver.caltech.edu/CaltechAUTHORS:HOUdmicm98", } @article {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/78863, title ="A Multiscale Finite Element Method for Elliptic Problems in Composite Materials and Porous Media", author = "Hou, Thomas Y. and Wu, Xiao-Hui", journal = "Journal of Computational Physics", volume = "134", number = "1", pages = "169-189", month = "June", year = "1997", doi = "https://doi.org/10.1006/jcph.1997.5682", url = "https://resolver.caltech.edu/CaltechAUTHORS:20170707-134035089", } @article {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/9080, title ="Convergence of a Boundary Integral Method for Water Waves", author = "Beale, J. Thomas and Hou, Thomas Y. and Lowengrub, John", journal = "SIAM Journal on Numerical Analysis", volume = "33", number = "5", pages = "1797-1843", month = "October", year = "1996", url = "https://resolver.caltech.edu/CaltechAUTHORS:BEAsiamjna96", } @article {CaltechAUTHORS_https://authors.library.caltech.edu/id/eprint/9081, title ="Second-Order Convergence of a Projection Scheme for the Incompressible Navier–Stokes Equations with Boundaries", author = "Hou, Thomas Y. and Wetton, Brian T. R.", journal = "SIAM Journal on Numerical Analysis", volume = "30", number = "3", pages = "609-629", month = "June", year = "1993", url = "https://resolver.caltech.edu/CaltechAUTHORS:HOUsiamjna93", }