Parallel SOR Iterative Algorithms and Performance Evaluation on a Linux Cluster

摘要

The successive over-relaxation (SOR) iterative method is an important solver for linear systems. In this paper, a parallel algorithm for the red-black SOR method with domain decomposition is investigated. The parallel SOR algorithm is designed by combining the traditional red-black SOR and row block domain decomposition technique, which reduces the communication cost and simplifies the parallel implementation. Two other iterative methods, Jacobi and Gauss-Seidel (G-S), ate also implemented in parallel for comparison. The three parallel iterative algorithms are implemented in C and MPI (Message Passing Interface) for solving the Dirichlet problem on a Linux cluster with eight dual processor 2.6ghz 32 bit Intel Xeons, totaling 16 processors. The performances of the three algorithms are evaluated in terms of speedup and efficiency.