A High-Order Discontinuous Galerkin Method for Electromagnetic Scattering From Perfectly Conducting Objects in Half-Space

A high-order discontinuous Galerkin (HODG) method based on surface integral equations is proposed for the analysis of electromagnetic scattering from complex perfect electrically conducting (PEC) objects situated in a half-space. The surface of the object is first partitioned into several subdomains, where nonconformal meshes with high-order (HO) curved elements are generated. Accordingly, the HO hierarchical vector (HOHV) basis functions are defined on the generated mesh in each subdomain. In addition, an extra set of HO mono-polar basis functions are introduced to account for the normal component of the current at the mesh discontinuities between adjacent subdomains. The current continuity is then weakly enforced by the discontinuous Galerkin (DG) formulation with interior penalty (IP) terms, which can be derived based on the half-space Green’s function. Owing to these penalty terms, a mixed-order modeling technique is further developed, where no local order matching is required at the order discontinuities. Thus, nonconformal mesh and/or basis functions with different orders can be freely used in the proposed HODG method, according to the geometrical features of the objects. Numerical results are presented to demonstrate the accuracy, efficiency, and flexibility of the proposed method.