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.

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Modelling, Analysis and Simulation [MAS]
Scientific Computing

Genseberger, M., Sleijpen, G. L. G., & van der Vorst, H. (2000). Using domain decomposition in the Jacobi-Davidson method. Modelling, Analysis and Simulation [MAS]. CWI.