SIE-DDM With Higher Order Hierarchical Vector Basis Functions for Solving Electromagnetic Problems on Multiscale Metallic Targets

Abstract

In this article, a nonconformal and nonoverlapping domain decomposition method (DDM) based on surface integral equation (SIE) is proposed for the electromagnetic (EM) scattering or radiation of multiscale metallic targets. To reduce the unknown amount of the conventional SIE for multiscale EM simulation, we apply curved triangular elements and higher order hierarchical vector (HOHV) basis functions to the SIE. Next, to increase the flexibility of geometrical modeling and accelerate the convergence of the presented SIE system for electrically large and multiscale metallic targets, a DDM scheme is further developed to employ a discontinuous Galerkin (DG) approach to glue conformal/nonconformal surface grids between adjacent subdomains. In addition, an interior penalty term is introduced to stabilize the DDM solution, and half edge-based HOHV basis functions are introduced to model the current associated with nonconformal surface elements. Meanwhile, the basis expansion and recombination (BER) technique is introduced to significantly accelerate the matrix-filling and improve the efficiency. The flexibility of basis order selection is further enhanced by the hierarchical characteristic of HOHV bases. Finally, several numerical results are provided to demonstrate the accuracy, efficiency, and flexibility of the proposed HO-DG-DDM.