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Stability of a Leap-Frog Discontinuous Galerkin Method for Time-Domain Maxwell's Equations in Anisotropic Materials

Part of: Equations of mathematical physics and other areas of application Partial differential equations, initial value and time-dependent initial-boundary value problems

Published online by Cambridge University Press:  27 March 2017

Adérito Araújo ,
Sílvia Barbeiro  and
Maryam Khaksar Ghalati
Adérito Araújo*
Affiliation:
CMUC, Department of Mathematics, University of Coimbra, Apartado 3008, EC Santa Cruz, 3001 – 501 Coimbra, Portugal
Sílvia Barbeiro*
Affiliation:
CMUC, Department of Mathematics, University of Coimbra, Apartado 3008, EC Santa Cruz, 3001 – 501 Coimbra, Portugal
Maryam Khaksar Ghalati*
Affiliation:
CMUC, Department of Mathematics, University of Coimbra, Apartado 3008, EC Santa Cruz, 3001 – 501 Coimbra, Portugal
*
*Corresponding author. Email addresses:alma@mat.uc.pt (A. Araújo), silvia@mat.uc.pt (S. Barbeiro), maryam@mat.uc.pt (M. Kh. Ghalati)
*Corresponding author. Email addresses:alma@mat.uc.pt (A. Araújo), silvia@mat.uc.pt (S. Barbeiro), maryam@mat.uc.pt (M. Kh. Ghalati)
*Corresponding author. Email addresses:alma@mat.uc.pt (A. Araújo), silvia@mat.uc.pt (S. Barbeiro), maryam@mat.uc.pt (M. Kh. Ghalati)
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Abstract

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 and error estimates, for cases of typical boundary conditions, either perfect electric, perfect magnetic or first order Silver-Müller. 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.

Keywords

Maxwell's equationsfully explicit leap-frog discontinuous Galerkin methodstability

MSC classification

Secondary: 35Q61: Maxwell equations 65M60: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
Type
Research Article
Information
Communications in Computational Physics , Volume 21 , Issue 5 , May 2017 , pp. 1350 - 1375
Copyright
Copyright © Global-Science Press 2017 

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