Book Section records
https://feeds.library.caltech.edu/people/Keller-H-B/book_section.rss
A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenTue, 16 Apr 2024 13:47:11 +0000A New Difference Scheme for Parabolic Problems
https://resolver.caltech.edu/CaltechAUTHORS:20170802-111549240
Authors: {'items': [{'id': 'Keller-H-B', 'name': {'family': 'Keller', 'given': 'Herbert B.'}}]}
Year: 1971
DOI: 10.1016/B978-0-12-358502-8.50014-1
This chapter discusses a new difference scheme for parabolic mixed initial-boundary value problems in one space dimension. The scheme has a number of very desirable features. It is simple, easy to program, and efficient. It is unconditionally stable and has second order accuracy with nonuniform nets. Richardson or h → 0 extrapolation is valid and yields two orders of accuracy improvement per extrapolation (with nonuniform nets). It is A-stable as well, that is, if the exact solution decays in time, so does the numerical scheme, with approximately the same rate; the data, coefficients, and solution need only be piecewise smooth and all the above remain valid. The method is also applicable to parabolic systems, to nonlinear parabolic equations, and even to some hyperbolic systems with special properties. The chapter presents the method, indicates the error estimates, h → 0 extrapolation and discusses an efficient algorithm for its application to the problem.https://authors.library.caltech.edu/records/y78z6-zxt85Buckling of Complete Spherical Shells under Slightly Nonuniform Loads
https://resolver.caltech.edu/CaltechAUTHORS:20170802-111028492
Authors: {'items': [{'id': 'Keller-H-B', 'name': {'family': 'Keller', 'given': 'Herbert B.'}}]}
Year: 1973
DOI: 10.1016/B978-0-12-215150-7.50010-7
This chapter discusses buckling of complete spherical shells under slightly nonuniform load. It presents the study of the axisymmetric deformations of a complete thin spherical shell subject to external loads, of the form p(θ) = p_0 + τ d(θ); θ is the latitude and τ measures the deviation of the load from a uniform pressure, p_0. The techniques for solving this and a broad class of related problems are quite new and particularly relevant in elasticity theory. Estimates of the error in any iterate can be given and the results also show that some specific perturbation schemes actually yield asymptotic results. The problem is formulated in the chapter based on a modification of the equations. The chapter presents the analysis that is applied to this finite case is elementary and easily shows how these methods yield a rigorous treatment using only the first two variations of the energy functional.https://authors.library.caltech.edu/records/ntgcf-15y18Finite difference methods for ordinary boundary value problems
https://resolver.caltech.edu/CaltechAUTHORS:20180829-073948869
Authors: {'items': [{'id': 'Keller-H-B', 'name': {'family': 'Keller', 'given': 'Herbert B.'}}]}
Year: 1976
DOI: 10.1007/BFb0120607
Finite difference methods have been shown to be extremely effective in the accurate and efficient solution of very general nonlinear two point boundary value problems. As with all practical numerical methods their development is tied very closely to the theoretical understanding of the procedures in question. Not surprisingly then there has been much current work on the theory of difference methods for two point problems. We shall recapitulate some of this theory here and also discuss some of the practical aspects in developing standard computer codes for such problems.https://authors.library.caltech.edu/records/5zvjr-4sg82Global Homotopies and Newton Methods
https://resolver.caltech.edu/CaltechAUTHORS:20170802-105839555
Authors: {'items': [{'id': 'Keller-H-B', 'name': {'family': 'Keller', 'given': 'Herbert B.'}}]}
Year: 1978
DOI: 10.1016/B978-0-12-208360-0.50009-7
This chapter describes the global homotopies and Newton methods. A key to devising global methods is to give up the monotone convergence and to consider more general homotopies. It turns out that singular matrices on the path cause no difficulties in the proof of Smales result. They cause trouble in attempts to implement this and most other global Newton methods numerically. Small steps must be taken in the neighborhood of vanishing Jacobians. This feature is not always pointed out in descriptions of the implementations but it is easily detected. These difficulties can be eliminated by using a somewhat different homotopy. The chapter discusses a pseudo-arc length continuation procedure in which the parameter is distance along a local tangent ray to the path. Using this parameter, this chapter discusses how to accurately locate the roots and the limit points on the path. These latter points are of great interest in many physical applications.https://authors.library.caltech.edu/records/24xxv-vpz22An Academic In Industry
https://resolver.caltech.edu/CaltechAUTHORS:20170802-105152260
Authors: {'items': [{'id': 'Keller-H-B', 'name': {'family': 'Keller', 'given': 'Herbert B.'}}]}
Year: 1979
DOI: 10.1016/B978-0-12-734250-4.50009-6
[no abstract]https://authors.library.caltech.edu/records/x9p1b-pmh90Steady State and Periodic Solution Paths: their Bifurcations and Computations
https://resolver.caltech.edu/CaltechAUTHORS:20201020-072658771
Authors: {'items': [{'id': 'Jepson-A-D', 'name': {'family': 'Jepson', 'given': 'A. D.'}}, {'id': 'Keller-H-B', 'name': {'family': 'Keller', 'given': 'H. B.'}}]}
Year: 1984
DOI: 10.1007/978-3-0348-6256-1_16
In this work we present a brief account of the theory and numerical methods for the analysis and Solution of nonlinear autonomous differential equations of the form
d/dτ w = f(w,λ,α); f:B₁×R²→B₂.https://authors.library.caltech.edu/records/c3s0q-j5k76Computations of Taylor Vortex Flows using multigrid continuation methods
https://resolver.caltech.edu/CaltechAUTHORS:20211104-064756963
Authors: {'items': [{'id': 'Dinar-Nathan', 'name': {'family': 'Dinar', 'given': 'Nathan'}}, {'id': 'Keller-H-B', 'name': {'family': 'Keller', 'given': 'Herbert B.'}}]}
Year: 1989
DOI: 10.1007/978-3-642-83733-3_9
Numerical solutions of axisymmetric Taylor vortex flows have been calculated using Multigrid Continuation Techniques. Both infinite and finite cylinders are considered, and the results agree well with experiments. New solutions are found in the infinite cylinder case and these, surprisingly, may help in understanding some experimental results obtained in relatively short cylinders. The numerical method proved to be efficient and reliable so that computations with fine grids and long cylinders are easily performed.https://authors.library.caltech.edu/records/b1ag5-nn127Parallel homotopy algorithm for large sparse generalized eigenvalue problems: Application to hydrodynamic stability analysis
https://resolver.caltech.edu/CaltechAUTHORS:20170802-124308426
Authors: {'items': [{'id': 'Chen-G', 'name': {'family': 'Chen', 'given': 'G.'}}, {'id': 'Keller-H-B', 'name': {'family': 'Keller', 'given': 'H. B.'}}, {'id': 'Lui-S-H', 'name': {'family': 'Lui', 'given': 'S. H.'}}, {'id': 'Roux-B', 'name': {'family': 'Roux', 'given': 'B.'}}]}
Year: 1992
DOI: 10.1007/3-540-55895-0_427
A parallel homotopy algorithm is presented for finding a few selected eigenvalues (for example those with the largest real part) of Az = λBz with real, large, sparse, and nonsymmetric square matrix A and real, singular, diagonal matrix B. The essence of the homotopy method is that from the eigenpairs of Dz = λBz, we use Euler-Newton continuation to follow the eigenpairs of A(t)z = λBz with A(t) ≡ (1−t)D + tA. Here D is some initial matrix and "time" t is incremented from 0 to 1. This method is, to a large degree, parallel because each eigenpath can be computed independently of the others. The algorithm has been implemented on the Intel hypcrcubc. Experimental results on a 64-nodc Intel iPSC/860 hypercube are presented. It is shown how the parallel homotopy method may be useful in applications like detecting Hopf bifurcations in hydrodynamic stability analysis.https://authors.library.caltech.edu/records/95g7p-gmb05