Using domain decomposition in the Jacobi-Davidson method
Menno Genseberger, Gérard L. G. Sleijpen, Henk A. van der Vorst · Centrum Wiskunde & Informatica (CWI), the national research institute for mathematics and computer science in the Netherlands · 2000
The Jacobi-Davidson method is suitable for computing solutions of large n-dimensional eigenvalue problems. It needs (approximate) solutions of specific n-dimensional linear systems. Here we propose a strategy based on a nonoverlapping domain decomposition technique in order to reduce the wall clock time and local memory requirements. For a model eigenvalue problem we derive optimal coupling parameters. Numerical experiments show the effect of this approach on the overall JacobiDavidson process. The implementation of the eventual process on a parallel computer is beyond the scope of this paper. Keywords: Eigenvalue problems, domain decomposition, Jacobi-Davidson, Schwarz method, nonoverlapping, iterative methods. 2000 Mathematics Subject Classification: 65F15, 65N25, 65N55. 1 Introduction The Jacobi-Davidson method [17] is a valuable approach for the solution of large (generalized) linear eigenvalue problems. The method reduces the large problem to a small one by projecting it...