Eigenvalues of Block Matrices Arising from Problems in Fluid Mechanics

Authors:
K. A. Cliffe;T. J. Garratt;A. Spence
Affiliations:
-;-;-
Venue:
SIAM Journal on Matrix Analysis and Applications
Year:
1994

Citing 0
Cited 3

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Inverse Iteration for Purely Imaginary Eigenvalues with Application to the Detection of Hopf Bifurcations in Large-Scale Problems

SIAM Journal on Matrix Analysis and Applications

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Abstract

Block matrices with a special structure arise from mixed finite element discretizations of incompressible flow problems. This paper is concerned with an analysis of the eigenvalue problem for such matrices and the derivation of two shifted eigenvalue problems that are more suited to numerical solution by iterative algorithms like simultaneous iteration and Arnoldi's method. The application of the shifted eigenvalue problems to the determination of the eigenvalue of smallest real part is discussed and a numerical example arising from a stability analysis of double-diffusive convection is described.