On the parallel iterative solution of linear systems arising in the FEAST algorithm for computing inner eigenvalues

Abstract

Methods for the solution of eigenvalue problems that are based on spectral projectors and contour integration have recently attracted more and more attention. Such methods require the solution of many shifted linear systems of full size. In most of the literature concerning these eigenvalue solvers, only few words are said on the solution of the linear systems, but they turn out to be very hard to solve by iterative linear solvers in practice. In this work we identify a row projection method for the solution of the inner linear systems encountered in the \feast algorithm and introduce a novel hybrid parallel and fully iterative implementation of the eigenvalue solver which exploits parallelism on several levels. We present numerical examples where graphene modeling is one of the target applications.