Chen, G. and Keller, H. B. and Lui, S. H. and Roux, B. (1992) Parallel homotopy algorithm for large sparse generalized eigenvalue problems: Application to hydrodynamic stability analysis. In: Parallel Processing: CONPAR 92—VAPP V. Lecture Notes in Computer Science. No.634. Springer , Berlin, pp. 331-342. ISBN 978-3-540-55895-8. https://resolver.caltech.edu/CaltechAUTHORS:20170802-124308426
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Abstract
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.
Item Type: | Book Section | |||||||||
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Additional Information: | © 1992 Springer-Verlag. Most of the work of the author (G. C) was done during a visit to the Center for Research on Parallel Computation at Caltech with support from "Conseil Régional Provence-Alpes-Côte d'Azur (France)". All the 64-node computations have been performed on the "Gamma" machine of the Caltech Concurrent Supercomputing Facilities. | |||||||||
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Series Name: | Lecture Notes in Computer Science | |||||||||
Issue or Number: | 634 | |||||||||
DOI: | 10.1007/3-540-55895-0_427 | |||||||||
Record Number: | CaltechAUTHORS:20170802-124308426 | |||||||||
Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20170802-124308426 | |||||||||
Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
ID Code: | 79770 | |||||||||
Collection: | CaltechAUTHORS | |||||||||
Deposited By: | Tony Diaz | |||||||||
Deposited On: | 02 Aug 2017 20:11 | |||||||||
Last Modified: | 15 Nov 2021 17:50 |
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