RESUMO
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. Therefore, the number of unknowns of the conventional DGVIE method can be further reduced. As a result, the memory of the proposed DGVIE method is only about half of the conventional one for inhomogeneous dielectric problems. Meanwhile, the total solution time has been reduced by the use of the proposed scheme. Particularly, the proposed DGVIE-SWG method is efficient in memory usage not only for inhomogeneous dielectric cases with high contrast ratio but also for cases with relatively low contrast ratio.
RESUMO
In this paper, electromagnetic scattering from dielectric objects with negative permittivity is solved by the volume integral equation (VIE)-hierarchical matrix (H-matrix)-based fast direct solver. To improve solution efficiency, a coarsening algorithm for the H-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. It is shown that scattering from inhomogeneous dielectric objects with negative permittivity and with multiscale structure can be analyzed efficiently by the DGVIE-H-matrix-based fast direct solver.