电磁散射的拉格朗日乘子区域分解算法

针对电磁散射问题,提出了一种基于广义变分原理的区域分解算法.将原求解区域划分为若干个不重叠的子区域,引入拉格朗日乘子法以满足相邻子区域之间场的连续性要求,并建立其修正泛函,使原问题转化为求解拉格朗日乘子.研究了子区域系数矩阵的可逆性.为了进一步提高效率,采用了重启的广义最小残量法为求解器.数值算例验证了本文方法的准确性和有效性.

Domain Decomposition Method with Lagrange Multipliers for the Analysis of Electromagnetic Scattering

A domain decomposition method (DDM) based on the generalized variational principle is presented for the analysis of electromagnetic scattering problems.The original computation domain is partitioned into nonoverlapping subdomains.Then the modified functional for the original problem was established with help of Lagrange multipliers,which also enforce the continuity conditions at the interface nodes between neighboring subdomains.The method leads to a reduced linear system of equations where only the Lagrange multipliers occur.The invertibility of the coefficient matrix on each subdomain is studied.To improve the algorithm further,the restarted generalized minimum residual method (GRMES) is used as the solver because of its superlinear convergence behavior.The proposed method is very efficient,in particular for the electrically large problems.The validity and computational efficiency have been verified by some numerical examples.