Parallel linear stationary iterative methods

A parallel linear stationary iterative method, defined by domain partitioning and referred to as the JSOR method, is analyzed in this paper. Basic JSOR convergence theorems, including one concerning the optimal relaxation parameter, are presented. JSOR is shown to have a much faster convergence rate than Jacobi and the same efficiency of interprocessor-data communication as Jacobi. Since JSOR contains the classic SOR and damped-Jacobi methods as its two extreme cases, the JSOR analysis can lead to a general linear stationary iteration theory, and imply both SOR and damped-Jacobi theories directly. Numerical results are presented to demonstrate the parallel performance of JSOR on a MIMD parallel computer. Finally, the development and application of JSOR are discussed.