A new version of conjugate gradient method parallel implementation

Abstract

In the article the authors describe an idea of parallel implementation of a conjugate gradient method in a heterogeneous PC cluster and a supercomputer Hitachi SR-2201. The new version of algorithm implementation differs from the one applied earlier (Jordan and Bycul, 2002), because it uses a special method for storing sparse coefficient matrices: only non-zero elements are stored and taken into account during computations, so that the sparsity of the coefficient matrix is taken full advantage of. The article includes a comparison of the two versions. A speedup of the parallel algorithm has been examined for three different cases of coefficient matrices resulting in solving different physical problems. The authors have also investigated a preconditioning method, which uses the inversed diagonal of the coefficient matrix, as a preconditioning matrix.