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Published 1992 | public
Book Section - Chapter

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

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.

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.

Additional details

Created:
August 20, 2023
Modified:
January 13, 2024