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A High-Order Time Domain Discontinuous Galerkin Method with Orthogonal Tetrahedral Basis for Electromagnetic Simulations in 3-D Heterogeneous Conductive Media

Part of: Partial differential equations, boundary value problems Numerical linear algebra

Published online by Cambridge University Press:  08 March 2017

Jun Yang ,
Wei Cai  and
Xiaoping Wu
Jun Yang
Affiliation:
Laboratory of Seismology and Physics of Earth's Interior, School of Earth and Space Sciences, University of Science and Technology of China, Hefei 230026, China Department of Mathematics and Statistics, University of North Carolina at Charlotte, Charlotte, NC 28223, USA
Wei Cai*
Affiliation:
Beijing Computational Science Research Center, Beijing 100193, Chin Department of Mathematics and Statistics, University of North Carolina at Charlotte, Charlotte, NC 28223, USA
Xiaoping Wu
Affiliation:
Laboratory of Seismology and Physics of Earth's Interior, School of Earth and Space Sciences, University of Science and Technology of China, Hefei 230026, China
*
*Corresponding author. Email addresses:wcai@uncc.edu, wcai@csrc.ac.cn (W. Cai)
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Abstract

We present a high-order discontinuous Galerkin (DG) method for the time domain Maxwell's equations in three-dimensional heterogeneous media. New hierarchical orthonormal basis functions on unstructured tetrahedral meshes are used for spatial discretization while Runge-Kutta methods for time discretization. A uniaxial perfectly matched layer (UPML) is employed to terminate the computational domain. Exponential convergence with respect to the order of the basis functions is observed and large parallel speedup is obtained for a plane-wave scattering model. The rapid decay of the out-going wave in the UPML is shown in a dipole radiation simulation. Moreover, the low frequency electromagnetic fields excited by a horizontal electric dipole (HED) and a vertical magnetic dipole (VMD) over a layered conductive half-space and a high frequency ground penetrating radar (GPR) detection for an underground structure are investigated, showing the high accuracy and broadband simulation capability of the proposed method.

Keywords

Maxwell's equationstime domaindiscontinuous Galerkin methodorthonormal polynomial basis functionstetrahedral elementsUPMLparallelization

MSC classification

Secondary: 65N30: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods 65F35: Matrix norms, conditioning, scaling 65F15: Eigenvalues, eigenvectors
Type
Research Article
Information
Communications in Computational Physics , Volume 21 , Issue 4 , April 2017 , pp. 1065 - 1089
Copyright
Copyright © Global-Science Press 2017 

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