Abstract

Introduction The diagonally preconditioned Conjugate Gradient Method (CGM) is commonly used in a range of applications for the iterative solution of Ax = b. The method lends itself to parallelisation by Domain Decomposition (DD) using a Single Program Multi-Data (SPMD) mapping onto Distributed Memory (DM) parallel platforms. While it is possible to achieve good parallel performance it is often the case that performance is limited by the communication performance of the parallel system. Performance of the parallel CGM method can be improved by reducing the impact of communication start-up latency and finite inter-processor communication bandwidth without modification of the algorithm. This invites an examination of the factors affecting parallel performance. Unstructured mesh applications using Finite Element or Finite Volume techniques to solve differential equations with iterative solution procedures are commonly parallelised using overlapping

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