Using Domain Decomposition in the

The Jacobi-Davidson method is suitable for computing solutions of large n-dimensional eigenvalue problems. It needs (approximate) solutions of speciic 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 eeect of this approach on the overall Jacobi-Davidson process. The implementation of the eventual process on a parallel computer is beyond the scope of this paper. 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 on an appropriate low dimensional subspace. Approximate solutions for eigenpairs of the large problem are obtained from the small problem by means of a Rayleigh-Ritz principle. The heart of the Jacobi-Davidson method is how the subspace is expanded. To keep the dimension of the subspace, and consequently the size of the small problem, low it is essential that all necessary information of the wanted eigenpair(s) is collected in the subspace after a small number of iterations. Therefore, the