A Discontinuous Galerkin Combined Field Integral Equation Formulation for Electromagnetic Modeling of Piecewise Homogeneous Objects of Arbitrary Shape

Abstract

We present a novel discontinuous Galerkin surface integral equation approach, based on the electric and magnetic current combined field integral equations (JMCFIE), for the electromagnetic analysis of arbitrarily shaped piecewise homogeneous objects. In the proposed scheme, nonoverlapping boundary surfaces and interfaces between materials can be handled independently, without any continuity requirement through multimaterial junctions and tear lines between surfaces in contact. The use of nonconformal meshes provides improved flexibility for CAD prototyping and tessellation. The proposed formulation can readily address nonconformal multi-material junctions, where three or more material regions meet. The continuity of the electric surface current across the junction contours is enforced by the combination of the boundary conditions implicit in the JMCFIE formulation and the weakly imposed interior penalty between the contacting surfaces within each region. This completely avoids the cumbersome junction problem, which no longer requires any special treatment. Numerical experiments are included to validate the accuracy and demonstrate the great versatility of the proposed JMCFIE-DG formulation for the management and solution of complex composite objects with junctions.