A Proposal of Cache-Cache Elements Technique of Eisenstat SSOR Preconditioning for Parallelism

Abstract

Eisenstat SSOR preconditioning for Krylov subspace methods is known to be very efficient compared with other preconditionings. However, Eisenstat SSOR preconditioning is not suited to parallel computation because it includes sequential process of computations as L^-1 and U^-1. Moreover, we cannot avoid these substantial computations on parallel computers. In this paper, we propose a Cache-Cache Elements technique of Eisenstat SSOR preconditioning for parallelism, and demonstrate its effectiveness through numerical experiments.