SIE-DDM Based on a Hybrid Direct–Iterative Approach for Analysis of Multiscale Problems

In this article, surface integral equation domain decomposition method (SIE-DDM) based on a hybrid direct-iterative approach is proposed for multiscale electromagnetic simulation. The solution of SIE-DDM matrix system is typically built on the strategy of inner-outer loop. Therefore, the direct approach is preferred to the subsolver in each decomposed domain. Here, a fast direct approach based on an enhanced hierarchically off-diagonal low-rank (HODLR) format involving extended admissibility condition (EAC) is present as an alternative subsolver, in which a reconstructing and recompression technique (RRT) is proposed. The efficiency and accuracy can be further improved by using this technology. The inverse of each subdomain is obtained by Sherman-Morrison-Woodbury algorithm (SMWA), while the global system is still solved by the iterative method. This hybrid framework makes full use of strengths of terative and direct approaches. On the other hand, the fast direct solver provides a robust preconditioner for the matrix system, especially for ill-conditioned cases. Several numerical examples will demonstrate the proposed method.