Parallel Homotopy Algorithm For Large Sparse Generalized Eigenvalue Problems: Application to Hydrodynamic Stability AnalysisReport as inadecuate




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1 Institut de Mécanique des Fluides de Marseille 2 CALTECH - California Institute of Technology 3 HKUST - Hong Kong University of Science and Technology

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 homotropy method is that from the eigenpairs of Dz = λBz, we use Euler-Newton continuation to follow the eigenpairs of Atz = λBz with At = 1−tD + 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-node 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.






Author: G.
Chen - H.B.
Keller - S.H.
Lui - B.
Roux -


Source: https://hal.archives-ouvertes.fr/



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