A Hybrid Conformal/Nonconformal Domain Decomposition Method for Multi-Region Electromagnetic Modeling

Abstract

This paper presents a unified framework for solving large-scale multi-region electromagnetic problems using a hybrid conformal/nonconformal domain decomposition method. In this method, an original electrically large problem is first divided into several regions based on its geometry. Each region is then meshed and further decomposed into smaller subdomains. As such, the decomposed problem is mesh-conformal and geometry-conformal within each region but could be mesh-nonconformal and geometry-nonconformal between two neighboring regions. To solve such a problem, a hybrid method is proposed that employs the finite-element tearing and interconnecting (FETI) method to deal with mesh-nonconformal and/or geometry-nonconformal interfaces, where a second-order transmission condition and a crosspoint correction technique are applied to improve the iterative convergence of the interface system and ensure a correct interconnection across subdomain interfaces. For mesh-conformal and geometry-conformal interfaces inside each region, the hybrid method employs the dual-primal finite element tearing and interconnecting (FETI-DP) method to construct an effective coarse grid correction for the interface problem. A unified global system of equations is finally formulated for the interface unknowns from both nonconformal and conformal interfaces. The proposed method is validated with simulation of wave propagation and radiation by broadband antennas and phased-array antennas covered with a radome and a near-field focal lens.