关键词: Poisson 方程, 交替方向隐式迭代格式, 矩阵方程

Abstract: In this paper, we improve the iterative scheme of alternating-direction implicit iterative method for Poisson equation, which reduces the difficulty and complexity of the calculating process by solving the lower dimension matrix equations in each iterative step. Taking the Gauss elimination method as an example, we estimate the computation of the improved alternating-direction implicit iterative scheme and find that the computation cost is much less than one of the classical alternating-direction implicit iterative scheme. Also, we prove the equivalence between the improved iterative scheme and the classical iterative scheme. Finally, we give the numerical tests to verify the advantage of the improved iterative scheme.

Key words: Poisson equation, alternating-direction implicit iterative scheme, matrix equation