A Mixed Discretization Scheme for Discontinuous Galerkin Domain Decomposition Method Applied to Surface Integral Equations

The discontinuous Galerkin (DG)-based domain decomposition method has been proposed for analyzing complex electromagnetic scattering problems. For targets involving material regions, the electric (J) and magnetic (M) current combined field integral equation (JMCFIE) is often used. Since JMCFIE integrates first- and second-kind Fredholm integral equations, its accuracy is lower compared to the one using only first-kind integral equations. To address this issue, this letter studies a mixed discretization scheme for the DG-JMCFIE, using Buffa-Christiansen (BC) functions and Rao-Wilton-Glisson (RWG) functions as testing functions. For the first time, we provide explicit formulations for BC functions on the boundaries of DG subdomains. We also introduce a novel interior penalty method to weakly enforce current continuity across subdomain boundaries within the BC-RWG mixed discretization scheme. Numerical experiments are conducted to evaluate the accuracy and convergence of our proposed method.