Stability of a leap-frog discontinuous Galerkin method for time-domain Maxwell's equations in anisotropic materials

In this work we discuss the numerical discretization of the time-dependent Maxwell's equations using a fully explicit leap-frog type discontinuous Galerkin method. We present a sufficient condition for the stability, for cases of typical boundary conditions, either perfect electric, perfect mag...

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Bibliographic Details
Published inarXiv.org
Main Authors Araújo, Adérito, Barbeiro, Sílvia, Maryam Khaksar Ghalati
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 21.07.2016
Subjects
Anisotropy
Boundary conditions
Computing time
Finite element method
Galerkin method
Mathematical analysis
Mathematical models
Mathematics - Numerical Analysis
Maxwell's equations
Model accuracy
Polynomials
Stability
Tensors
Time dependence
Time domain analysis
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Summary:In this work we discuss the numerical discretization of the time-dependent Maxwell's equations using a fully explicit leap-frog type discontinuous Galerkin method. We present a sufficient condition for the stability, for cases of typical boundary conditions, either perfect electric, perfect magnetic or first order Silver-M\"uller. The bounds of the stability region point out the influence of not only the mesh size but also the dependence on the choice of the numerical flux and the degree of the polynomials used in the construction of the finite element space, making possible to balance accuracy and computational efficiency. In the model we consider heterogeneous anisotropic permittivity tensors which arise naturally in many applications of interest. Numerical results supporting the analysis are provided.
ISSN:2331-8422
DOI:10.48550/arxiv.1607.06425