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

• Published in: IEEE transactions on antennas and propagation Vol. 70; no. 1; pp. 487 - 498
• Main Authors: Martin, Victor F., Landesa, Luis, Obelleiro, Fernando, Taboada, Jose M.
• Format: Journal Article
• Language: English
• Published: New York IEEE 01-01-2022; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Antennas; Boundary conditions; CAD; Computer aided design; Discontinuous Galerkin (DG) method; electric and magnetic currents combined field integral equation (JMCFIE); Electric contacts; Electrical junctions; fast solvers; Galerkin method; Integral equations; Junctions; Magnetic tunneling; Materials handling; Method of moments; method of moments (MoM); multilevel fast multipole algorithm (MLFMA); piecewise homogeneous objects; Prototyping; Surface impedance; Surface treatment; Tessellation
• ISSN: 0018-926X; 1558-2221
• DOI: 10.1109/TAP.2021.3098549

We present a novel discontinuous Galerkin (DG) 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 computer-aided-design (CAD) prototyping and tessellation. The proposed formulation can readily address nonconformal multimaterial 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 (IP) 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.