Discontinuous Galerkin methods for dispersive and lossy Maxwell’s equations and PML boundary conditions
نویسندگان
چکیده
In this paper, we will present a unified formulation of discontinuous Galerkin method (DGM) for Maxwell’s equations in linear dispersive and lossy materials of Debye type and in the artificial perfectly matched layer (PML) regions. An auxiliary differential equation (ADE) method is used to handle the frequency-dependent constitutive relations with the help of auxiliary polarization currents in the computational and PML regions. The numerical flux for the dispersive lossy Maxwell’s equations with the auxiliary polarization current variables is derived. Various numerical results are provided to validate the proposed formulation. 2004 Elsevier Inc. All rights reserved.
منابع مشابه
Reflection/transmission Characteristics of a Discontinuous Galerkin Method for Maxwell’s Equations in Dispersive Inhomogeneous Media
In this paper, we analyze the transmission and reflection properties of a high order discontinuous Galerkin method for dispersive Maxwell’s equations, originally proposed by Lu et al. [J. Comput. Phys. 200 (2004), pp. 549-580]. We study the reflection and transmission properties of the numerical method for up to second-order polynomial elements for oneand two-dimensional Maxwell’s equations wit...
متن کاملMaxwell’s Equations with Impedance Boundary Conditions: Discontinuous Galerkin and Reduced Basis Methods
We consider Maxwell’s equations with impedance boundary conditions on a polyhedron with polyhedral holes. Well-posedness of the variational formulation is proven and a discontinuous Galerkin (dG) approximation is introduced. We prove well-posedness of the dG problem as well as a priori error estimates. Next, we use the frequency ω as a parameter in a multi-query context. For this purpose, we de...
متن کاملConvergence of a Discontinuous Galerkin scheme for the mixed time domain Maxwell’s equations in dispersive media
This study is concerned with the solution of the time domain Maxwell’s equations in a dispersive propagation media by a Discontinuous Galerkin Time Domain (DGTD) method. The Debye model is used to describe the dispersive behaviour of the media. The resulting system of equations is solved using a centered flux discontinuous Galerkin formulation for the discretization in space and a second order ...
متن کاملDiscontinuous Galerkin Time Domain Methods in Computational Electrodynamics: State of the Art
This text reviews the state of the art of the Discontinuous Galerkin (DG) method applied to the solution of the Maxwell’s equations in Time Domain (TD). The work is divided into two parts. In the first part, the mathematical formulation of the DGTD method, together with a review and a discussion on the different ways to implement it is presented. The second part presents models and techniques t...
متن کاملThe Time-Harmonic Discontinuous Galerkin Method as a Robust Forward Solver for Microwave Imaging Applications
Novel microwave imaging systems require flexible forward solvers capable of incorporating arbitrary boundary conditions and inhomogeneous background constitutive parameters. In this work we focus on the implementation of a time-harmonic Discontinuous Galerkin Method (DGM) forward solver with a number of features that aim to benefit tomographic microwave imaging algorithms: locally varying high-...
متن کامل