Comparisons of Different Interior Penalty Terms on Discontinuous Galerkin-based Mixed Potential Integral Equation

The traditional mixed potential integral equation (MPIE) technique encounters difficulties in generating conformal meshes and suffers from poor computational efficiency due to the large number of unknowns involved when analyzing complex multi-scale targets in the half-space. A non-conformal mesh-based discontinuous Galerkin (DG) method for electromagnetic scattering problems in half-space recently proposed to improve computational efficiency. In this report, the influence of different interior penalty (IP) terms on the condition number of the system matrix and the accuracy of computed results is compared. A flexible IP term with improved convergence performance is proposed, eliminating the need to search for shared contours on non-conformal meshes, especially on curved surfaces. Several numerical examples in the half-space are simulated to validate the accuracy and efficiency.