Decreasing the memory of the discontinuous Galerkin volume integral equation method for scattering from inhomogeneous dielectric objects.

A memory-efficient implementation scheme for the discontinuous Galerkin volume integral equation method (DGVIE) using Schaubert-Wilton-Glisson (SWG) basis functions is proposed to analyze electromagnetic scattering from inhomogeneous dielectric objects. For this proposed scheme, almost no half-SWG basis functions are needed for the elements separating nonconformal meshes, while these half-SWG basis functions are indispensable for the conventional DGVIE-SWG method. This is realized by applying the divergence-free condition of the electric displacement vector explicitly for nonconformal meshes separating neighboring subdomains of an inhomogeneous dielectric body.

Direct solution of the volume integral equation for electromagnetic scattering from dielectric objects with negative permittivity.

In this paper, electromagnetic scattering from dielectric objects with negative permittivity is solved by the volume integral equation (VIE)-hierarchical matrix (-matrix)-based fast direct solver. To improve solution efficiency, a coarsening algorithm for the -matrix is used, and the key parameter for the admissible condition is optimized through numerical experiments. Finally, the discontinuous Galerkin (DG) VIE (DGVIE) method is developed for the fast direct solver.