A Novel Discontinuous Galerkin Time-Domain Method for Electromagnetic Scattering Analysis From Full-Tensor Anisotropic Materials

In this paper, we propose a general discontinuous Galerkin time-domain (DGTD) method for analyzing electromagnetic scattering from full-tensor anisotropic materials, both lossy and lossless. This proposed DGTD method for anisotropic materials incorporates numerical flux for connecting neighboring elements using tensor-based wave impedance and admittance matrices, offering greater versatility compared to traditional methods for full-tensor materials. For lossy anisotropic materials, the complex permittivity tensor is decomposed into a real permittivity tensor and a conductivity tensor to facilitate implementation. The wave impedance and wave admittance are rigorously derived from the permittivity and permeability tensors. To enhance the accuracy and efficiency of the DGTD method, second-order nodal basis functions are employed in the electromagnetic scattering solver for anisotropic materials. The validity and performance of this solver are demonstrated through several numerical examples involving electromagnetic scattering problems in anisotropic materials.