Domain Decomposition Methods for Finite Element Analysis of Large-Scale Electromagnetic Problems

This chapter presents domain decomposition methods (DDMs) based on the dual-primal finite element tearing and interconnecting (FETI-DP) algorithm for the full-wave analysis of large-scale electromagnetic problems governed by linear systems with millions or even billions of unknowns. It first reviews the original FETI-DP formulation with one Lagrange multiplier and a later version using two Lagrange multipliers with a Robin boundary condition for faster high-frequency convergence. Recent developments are then presented to (1) relax the conformal interface mesh requirement, (2) accelerate convergence, and (3) improve truncation accuracy. These include two nonconformal FETI-DP methods, higher-order transmission conditions for evanescent modes, and a hybrid FETI/FETI-DP scheme for multi-region problems. Numerical results for wave propagation, finite antenna arrays, radomes, and optical devices validate the accuracy, efficiency, and capability of the proposed algorithms.