对称区域分裂法解一类交接面问题

Symmetric Domain Decomposition(SDD)Method Applied to Interface Problems

本文考察用对称区域分裂法来解比较一般的“对称”交接面问题,而以普通的偏微分方程边值问题作为它的特例.文中提供了三种算法,包括改进的区域分裂法.运用这些算法,原问题可化为两个或四个具半规模的子问题,而各子问题不再是具有奇异性的交接面问题.所有算法均可在多机(multiprocessor及multicomputer)上完全并行,且通讯量极少.文末给出了三种算法的数值试验结果.

In this paper, the SDD method is extended and utilized to solve general 'symmetric' interface problems (or transmission problems) with constant junction coefficients. Three kinds of algorithms are provided, including an improved SDD procedure. By using these algorithms, the original problem can be transformed into two or four subproblems of 'half' size, which can be performed fairly on multiprocessors or multicomputers. As a background, the model interface problem is constructively discussed. And for general problems, both the continuous and discrete cases are conidered. All the concerned subproblems are no more of interface type, but only common boundary-value problems. Some numerical results are presented.