Stability of a Leap-Frog Discontinuous Galerkin Method for Time-Domain Maxwell's Equations in Anisotropic Materials. (27th March 2017)

• Record Type: Journal Article
• Authors: Araújo, Adérito; Barbeiro, Sílvia; Ghalati, Maryam Khaksar
• Is Part Of: Communications in computational physics. Volume 21:Number 5(2017:May)
• Page Start: 1350
• Page End: 1375
• Publication Date: 2017-03-27
• Subjects: 35Q61, -- 65M60; Maxwell's equations, -- fully explicit leap-frog discontinuous Galerkin method, -- stability; Mathematical physics -- Data processing -- Periodicals; Physics -- Data processing -- Periodicals; 530.150285
• DOI: 10.4208/cicp.OA-2016-0110
• Languages: English
• ISSNs: 1815-2406

Abstract

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.