A preconditioned dual-primal finite element tearing and interconnecting method for solving three-dimensional time-harmonic Maxwell's equations

A new preconditioned dual-primal nonoverlapping domain decomposition method is proposed for the finite element solution of three-dimensional large-scale electromagnetic problems. With the aid of two Lagrange multipliers, the new method converts the original volumetric problem to a surface problem by using a higher-order transmission condition at the subdomain interfaces to significantly improve the convergence of the iterative solution of the global interface equation. Similar to the previous version, a global coarse problem related to the degrees of freedom at the subdomain corner edges is formulated to propagate the residual error to the whole computational domain at each iteration, which further increases the rate of convergence. In addition, a fully algebraic preconditioner based on matrix splitting is constructed to make the proposed domain decomposition method even more robust and scalable. Perfectly matched layers (PMLs) are considered for the boundary truncation when solving open-region problems. The influence of the PML truncation on the convergence performance is investigated by examining the convergence of the transmission condition for an interface inside the PML. Numerical examples including wave propagation and antenna radiation problems truncated with PMLs are presented to demonstrate the validity and the capability of this method. (C) 2014 Elsevier Inc. All rights reserved.