Half-Sweep Arithmetic Mean Method for Solving 2D Elliptic Equation

摘要

This paper presents our study on combining the half-sweep iteration technique with the two-stage Arithmetic Mean (AM) method namely Half-Sweep Arithmetic Mean (HSAM) method in solving 2D elliptic equation. Recently, the HSAM method was studied extensively since it was very suitable for parallel implementation on a multiprocessor system. In the previous works, its great potential was demonstrated in solving partial differential equations (PDEs) mainly in one dimensional space. In this study, several numerical experiments were carried out to examine the efficiency of the suggested HSAM method in solving PDEs in two dimensional space. The implementation of the Full-Sweep Arithmetic Mean (FSAM) method is also provided. For performance comparison, the implementations of the standad Full-Sweep Gauss-Seidel (FSGS) and Half-Sweep Gauss-Seidel (HSGS) methods are presented.