Parallel Performance Studies for a Parabolic Test Problem

Abstract

The performance of a parallel computer depends on an intricate interplay of the processors, the architecture of the compute nodes, their interconnect network, the numerical algorithm, and the scheduling policy used. This note considers a parabolic test problem given by a time-dependent linear reaction-diffusion equation in three space dimensions, whose spatial discretization results in a large system of ordinary differential equations. These are integrated in time by the family of numerical differentiation formulas, which requires the solution of a system of linear equations at every time step. The results presented here show excellent performance on the cluster hpc in the UMBC High Performance Computing Facility and confirm that it is beneficial to use all four cores of the two dual-core processors on each node simultaneously, giving us in effect a computer that can run jobs efficiently with up to 128 parallel processes.