基于积分方程区域分解算法的研究进展

The progress of domain decomposition method based on integral equation

介绍了近年来用于电磁建模的积分方程区域分解算法(domain decomposition method,DDM).DDM是一种基于“分而治之”策略的框架性算法,为复杂电磁问题的求解提供了一种灵活的技术途径.结合国内外研究动态详细介绍了三类积分方程DDM,即重叠型积分方程DDM,非共形、非重叠型积分方程DDM以及基于等效原理的积分方程DDM,并通过数值算例说明了这些算法的优缺点.最后总结了积分方程DDM的主要挑战以及展望.

This paper presents the domain decomposition method based on integral equation(IE-DDM)for electromagnetic modeling in recent years.Domain decomposition method is a framework algorithm relied on the strategy of divide and conquer,which provides a flexible approach for solving complex electromagnetic problems.With the domestic and foreign research trends,three kinds of domain decomposition algorithms based on integral equation are particularly reviewed in this paper,namely,overlapping IE-DDM,non-conformal,non-overlapping IE-DDM and equivalence principle algorithm(EPA).Numerical examples are given to illustrate the advantages and disadvantages of these algorithms.Finally,the main challenges and prospects of the domain decomposition method of integral equation are summarized.