A Local Coupling Multi-Trace Domain Decomposition Method for Electromagnetic Scattering from Multilayered Dielectric Objects

Abstract

In this paper, a local coupling multi-trace domain decomposition method (LCMT-DDM) based on surface integral equation (SIE) formulations is proposed to analyze electromagnetic scattering from multilayered dielectric objects. Different from the traditional SIE-DDM, where the interactions between sub-domains are accounted for using global radiation coupling, LCMT-DDM uses a local coupling scheme. The original multilayered object is decomposed into several independent domains, i.e. the exterior region (free space) and many homogeneous interior regions (dielectrics). The boundaries of sub-domains are all touching-faces, where only the Robin transmission conditions (RTCs) are enforced to ensure the field continuity. Hence, each sub-domain only couples with its neighboring regions, which makes the DDM system a highly sparse matrix especially when the number of sub-domains is large. In each sub-domain, the electric field integral equation (EFIE) and the magnetic field integral equation (MFIE) for dielectrics are used as the governing equations. By imposing RTCs, well-conditioned equations are formed in each sub-domain without invoking the combined field integral equation (CFIE), which usually causes accuracy issues in dielectric modeling. Since the sub-domain matrices are diagonally dominant, the flexible generalized minimal residual (FGMRES) technique is used to accelerate the iterative solution of the whole DDM system. Moreover, an effective preconditioner that can be recursively constructed is proposed.