CGMN and CARP-CG on clusters of multi-core CPUs

Abstract

In 1979, Bj\"orck and Elfving published some remarkably robust CG-accelerated row projection methods. More recently, Gordon and Gordon proposed a parallel variant called CARP-CG (Component-Averaged Row Projections). We adopt their idea for the inter-node parallelisation but also show that a more conventional multi-coloring technique yields a simpler and more memory efficient implementation when it comes to fine-grained parallelism. The method is studied in the context of convection-dominated PDEs, the Helmholtz equations and inner eigenvalue computations. Some performance aspects are discussed and scalability up to several thousand cores is shown.