A New Dual-Primal Domain Decomposition Approach for Finite Element Simulation of 3-D Large-Scale Electromagnetic Problems

Abstract

A novel dual-primal non-overlapping domain decomposition method (DDM) for the finite element solution of three-dimensional (3D) large-scale electromagnetic problems is proposed. This method reduces the computational complexity from solving the original 3D problem to an equivalent interface problem by utilizing the idea of the dual-primal finite element tearing and interconnecting (FETI-DPEM) method. The new method, which is referred to as the FETI-DPEM2, combines the dual-primal idea with two Lagrange multipliers and implements Robin-type transmission condition at the subdomain interfaces to significantly improve the convergence of the interface solution in the high-frequency region. Similar to the original version, a global coarse problem related to the degrees of freedom at the subdomain corner edges is designed to propagate the residual error to the whole computational domain at each iteration, which further increases the convergence. Numerical examples are presented to demonstrate the validity and the capability of this method. The results show that the proposed method produces fast solutions to large-scale problems in any frequency band.