An Improved Subdomain Level Nonconformal Discontinuous Galerkin Time Domain (DGTD) Method for Materials With Full-Tensor Constitutive Parameters

Abstract

Ultrawideband simulation of negative refraction in bicrystals is important for the design optimization of devices involving such anisotropic media, but it is a nontrivial task, especially when low-order methods are utilized. This work proposes an improved discontinuous Galerkin time domain (DGTD) method for simulating time-dependent electromagnetic fields for inhomogeneous media with full anisotropic constitutive parameters (full anisotropic media). It employs the electric field intensity ${\mathbf E}$ and magnetic flux density ${\mathbf B}$ to solve Maxwell's equations. The ${\mathbf EB}$ -scheme-based anisotropic Riemann solver and nonconformal mesh are employed for domain decomposition to allow efficient spatial discretization. An unsplit-field Maxwellian multiaxial perfectly matched layer for full anisotropic media is derived and shown to be effective to absorb outgoing waves and suppress the potential late-time instability found in classical PML. In addition, the total-field/scattered-field technique is further studied to allow a nonconformal mesh, vector basis functions, and half-space situation. This newly improved DGTD method is validated with test cases and applied to the negative reflection in YVO $_{4}$ bicrystal.