Computing Eigenvalues Occurring in Continuation Methods with the Jacobi–Davidson QZ Method
✍ Scribed by Jos L.M. van Dorsselaer
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 480 KB
- Volume
- 138
- Category
- Article
- ISSN
- 0021-9991
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✦ Synopsis
Continuation methods are well-known techniques for computing several stationary solutions of problems involving one or more physical parameters. In order to determine whether a stationary solution is stable, and to detect the bifurcation points of the problem, one has to compute the rightmost eigenvalues of a related, generalized eigenvalue problem. The recently developed Jacobi-Davidson QZ method can be very effective for computing several eigenvalues of a given generalized eigenvalue problem. In this paper we will explain how the Jacobi-Davidson QZ method can be used to compute the eigenvalues needed in the application of continuation methods. As an illustration, the two-dimensional Rayleigh-Be ´nard problem has been studied, with the Rayleigh number as a physical parameter. We investigated the stability of stationary solutions, and several bifurcation points have been detected. The Jacobi-Davidson QZ method turns out to be very efficient for this problem.