A parallel solver for extreme eigenpairs

Abstract

In this paper a parallel algorithm for finding a group of extreme eigenvalues is presented. The algorithm is based on the well known Davidson method for finding one eigenvalue of a matrix. Here we incorporate knowledge about the structure of the subspace through the use of an arrowhead solver which allows more parallelization in both the original Davidson and our new version. In our numerical results various preconditioners (diagonal, multigrid and ADI) are compared. The performance results presented are for the Paragon but our implementation is portable to machines which provide MPI and BLAS.