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

Abstract

This thesis deals with the computation of a small set of exterior eigenvalues of a given large sparse matrix on present (and future) supercomputers 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. The performance of block vector computations is analyzed on the node-level as well as for a cluster of nodes. The implementation of the method is based on an existing sparse linear algebra framework and exploits several layers of parallelism. Numerical tests show that the block method developed 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.