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 E and magnetic flux density B to solve Maxwell's equations. The 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 YVO4 bicrystal.

Keywords

• Discontinuous Galerkin time domain (DGTD) method
• multiaxial PML (M-PML)
• non-conformal mesh
• negative refraction
• $_{4}$ bicrystal%22%2C%22default_operator%22%3A%22AND%22%7D%7D%7D"> YVO<named-content xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" content-type="math" xlink:type="simple"> <inline-formula> <tex-math notation="LaTeX">$_{4}$</tex-math> </inline-formula> </named-content> bicrystal