Broadband surface impedance boundary conditions for higher order time domain discontinuous Galerkin method

Broadband surface impedance boundary conditions for higher order time domain discontinuous... Purpose – The purpose of this paper is to present a time domain discontinuous Galerkin (DG) approach for modeling wideband frequency dependent surface impedance boundary conditions. Design/methodology/approach – The paper solves the Maxwellian initial value problem in a computational domain, which is spatially discretized by the higher order DG method. On the boundary of the computational domain the paper applies a suitable impedance boundary condition (IBC). The frequency dependency of the impedance function is modeled by auxiliary differential equations (ADE). Findings – The authors will study the resonance frequency and the Q factor of different types of cavity resonators including lossy materials. The lossy materials are modeled by means of IBCs. The authors will compare the results with analytical results, as well as numerical results obtained by direct calculations where lossy materials are included explicitly into the numerical model. Several convergence studies are performed which demonstrate the accuracy of the approach. Originality/value – Modeling of frequency dependent boundary conditions in time domain with finite difference time domain method (FDTD) method is considered in numerous papers, as well as in frequency domain finite element method (FEM), and in a few papers also time domain FEM. However, FDTD method is only first order accurate and fails in modeling of complicated surfaces. FEM allows for high order accuracy, but time domain modeling is numerically extremely expensive. In frequency domain, broadband modeling of frequency dependent boundary conditions requires several simulations as opposed to the time domain, where a single simulation is needed. The time domain DG method proposed in this paper allows to overcome the difficulties. The authors introduce a broadband surface impedance formulation based on the ADE approach for the higher order DG method. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering Emerald Publishing

Broadband surface impedance boundary conditions for higher order time domain discontinuous Galerkin method

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Publisher
Emerald Publishing
Copyright
Copyright © 2014 Emerald Group Publishing Limited. All rights reserved.
ISSN
0332-1649
DOI
10.1108/COMPEL-08-2013-0260
Publisher site
See Article on Publisher Site

Abstract

Purpose – The purpose of this paper is to present a time domain discontinuous Galerkin (DG) approach for modeling wideband frequency dependent surface impedance boundary conditions. Design/methodology/approach – The paper solves the Maxwellian initial value problem in a computational domain, which is spatially discretized by the higher order DG method. On the boundary of the computational domain the paper applies a suitable impedance boundary condition (IBC). The frequency dependency of the impedance function is modeled by auxiliary differential equations (ADE). Findings – The authors will study the resonance frequency and the Q factor of different types of cavity resonators including lossy materials. The lossy materials are modeled by means of IBCs. The authors will compare the results with analytical results, as well as numerical results obtained by direct calculations where lossy materials are included explicitly into the numerical model. Several convergence studies are performed which demonstrate the accuracy of the approach. Originality/value – Modeling of frequency dependent boundary conditions in time domain with finite difference time domain method (FDTD) method is considered in numerous papers, as well as in frequency domain finite element method (FEM), and in a few papers also time domain FEM. However, FDTD method is only first order accurate and fails in modeling of complicated surfaces. FEM allows for high order accuracy, but time domain modeling is numerically extremely expensive. In frequency domain, broadband modeling of frequency dependent boundary conditions requires several simulations as opposed to the time domain, where a single simulation is needed. The time domain DG method proposed in this paper allows to overcome the difficulties. The authors introduce a broadband surface impedance formulation based on the ADE approach for the higher order DG method.

Journal

COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic EngineeringEmerald Publishing

Published: Jul 1, 2014

Keywords: Auxiliary differential equations; Discontinuous Galerkin method; Surface impedance boundary conditions; Time domain modeling

References

  • Discontinuous Galerkin time‐domain solution of Maxwell's equations on locally‐refined nonconforming Cartesian grids
    Canouet, N.; Fezoui, L.; Piperno, S.
  • On the skin effect approximation
    Smith, G.S.

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