Towards a fast parallel sparse symmetric matrix–vector multiplication

Abstract

The sparse matrix–vector product is an important computational kernel that runs ineffectively 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.