Distributed solution of high-order compact difference schemes for multidimensional convection-diffusion equations

Abstract

The performance of a high-order compact (HOC) discretisation of a multidimensional time dependent convection-diffusion equation on a distributed computer cluster is demonstrated. We consider a D dimensional fourth-order compact difference scheme and concurrently solve the implicit equation with GMRES(m). The performance of GMRES(m) on distributed computers is limited by the inter-processor communication required by the matrix-vector multiplication. It is shown that the compact scheme requires approximately half the number of communications as a non-compact difference scheme of the same order of truncation error. As the dimensionality is increased, the ratio of computation that can be overlapped with communication also increases. CPU times and parallel efficiency graphs for single time step approximation of up to 7D HOC coarse approximations demonstrate improved parallel scalability over non-compact difference schemes. © Springer-Verlag 2003.