Using domain decomposition in the Jacobi-Davidson method

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 Jacobi-Davidson process. The implementation of the eventual process on a parallel computer is beyond the scope of this paper.