Towards a fast parallel sparse symmetric matrix--vector multiplication

摘要

The sparse matrix-vector product is an important computational kernel that runs ineffec- tively on many computers with super-scalar RISC processors. In this paper we analyse the performance of the sparse matrix--vector product with symmetric matrices originating from the FEM and describe techniques that lead to a fast implementation. It is shown how these optimisations can be incorporated into an efficient parallel implementation using message- passing. We conduct numerical experiments on many different machines and show that our optimisations speed up the sparse matrix--vector multiplication substantially.