Parallel solution of large sparse eigenproblems using a Block-Jacobi-Davidson method

Abstract

This talk discusses the computation of a small set of exterior eigenvalues of a large sparse matrix using a Block-Jacobi-Davidson method. The main idea of the method is to operate on blocks of vectors and to combine several sparse matrix-vector multiplications with different vectors in a single computation. Block vector calculations and in particular sparse matrix-multiple-vector multiplications can be considerably faster than single vector operations if a suitable memory layout is used for the block vectors. Numerical tests show that the block method works well for a wide range of matrices and that a small block size can speed up the complete computation of a set of eigenvalues significantly in comparison to a single vector calculation.