Improving the parallel performance of a domain decomposition preconditioning technique in the Jacobi–Davidson method for large scale eigenvalue problems

Most computational work in Jacobi–Davidson [G.L.G. Sleijpen, H.A. van der Vorst, A Jacobi–Davidson iteration method for linear eigenvalue problems, SIAM J. Matrix Anal. Appl. 17 (1996) 401–425], an iterative method for large scale eigenvalue problems, is due to a so-called correction equation. In [M. Genseberger, G.L.G. Sleijpen, H.A. van der Vorst, Domain decomposition in Jacobi–Davidson for PDE related eigenvalue problems, in preparation] a strategy for the approximate solution of the correction equation was proposed. This strategy is based on a domain decomposition preconditioning technique in order to reduce wall clock time and local memory requirements. This paper discusses the aspect that the original strategy can be improved. For large scale eigenvalue problems that need a massively parallel treatment this aspect turns out to be nontrivial. The impact on the parallel performance will be shown by results of scaling experiments up to 1024 cores.