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Parallel homotopy algorithm for large sparse generalized eigenvalue problems: Application to hydrodynamic stability analysis

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
Related URLs:
URLURL TypeDescription
https://doi.org/10.1007/3-540-55895-0_427DOIArticle
https://rdcu.be/b4ct4PublisherFree ReadCube access
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.
Funders:
Funding AgencyGrant Number
Conseil Régional Provence-Alpes-Côte d'AzurUNSPECIFIED
Series Name:Lecture Notes in Computer Science
Issue or Number:634
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 May 2020 18:04

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