A compression scheme for domain decomposition method in solving electromagnetic problems

Abstract

A compression framework is presented for improving the domain decomposition method (DDM) in solving Maxwell's equations. Because the DDM heavily relies on the numerical computation at the subdomain interfaces, the proposed approach focuses on effectively generating the boundary and port solutions of the subdomains. In each subdomain, the original building block is decomposed into a number of subblocks by the nested dissection method. The boundary matrices of the subblocks are compressed as hierarchical matrices and merged into larger ones with respect to the partition tree. Combining with the finite element tearing and interconnecting technique, the original DDM system can be transformed into an interface relation enabling fast matrix operations. Moreover, the memory consumption of DDM is also reduced as only the interface unknowns are kept in the solution process. The accuracy and efficiency of the proposed method are studied and compared with direct DDM method through several numerical examples.