无界扇形外区域多子域非重叠区域分解算法

Non-overlapping domain decomposition method for multi-sub-domain in unbouded fanshaped outer domain

本文主要研究了无界扇形外区域多子域的区域分解算法。在自然边界规划的基础上,以椭圆方程的混合边值问题为例,提出了多子域非重叠区域D-N交替算法。将该算法的区域分解成相应的几个子域,分析了该算法的离散格式和变分形式。由于该算法与Richardson迭代法是等价的,通过证明Richardson迭代法是收敛的,进一步验证了该算法也是收敛的,并且与网格参数h无关。

In this paper, an non-overlapping domain decomposition method for multisubdomain in unbouded fan- shaped outer domain is studied. Based on the natural boundary, the D- N alternating method of mixed boundary value problems for elliptic equations in multi-sub-domain case is advanced. Planning domain shape and writing algorithm, the discrete scheme and variational form of the algorithm are analyzed.Since the algorithm and the Richardson iteration method are equivalent, the convergence of the Richardson iteration method is proved to be convergent, and it is independent of the mesh parameter h.