Parallel SOR Iterative Algorithms and Performance Evaluation on a Linux Cluster

The successive over-relaxation (SOR) how to quickly verify and generate a iterative method is an important solver for linear multicoloring ordering according to the given systems. In this paper, a parallel algorithm for the structure of a matrix or a grid. However, the red-black SOR method with domain decomposition is multi-color SOR method is parallel only within investigated. The parallel SOR algorithm is designed the same color. For some problems such as two by combining the traditional red-black SOR and row block domain decomposition technique, which reduces the communication cost and simplifies the parallel Poisson equations, the Red-Black two-color SOR implementation. Two other iterative methods, Jacobi method is preferred. Yanheh [4] showed that the and Gauss-Seidel(G-S), are also implemented in Red-Black SOR method is more efficient and parallel for comparison. The three parallel iterative smoother than the sequential SOR method. Xie algorithm are implemented in C and MPI (Message proposed an efficient parallel SOR method Passing Interface) for solving the Dirichlet problem (PSOR) using domain decomposition and on a Linux cluster with eight dual processor 2.6ghz 32 interprocessor data communication techniques bit Intel Xeons, totaling 16 processors. The [5]. It is shown that PSOR is just the SOR performances of the three algorithms are evaluated in method applied to a reordered linear system, so terms of speedup and efficiency. that the theory of SOR can also be applied to the