期刊
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
卷 234, 期 4, 页码 1088-1096出版社
ELSEVIER SCIENCE BV
DOI: 10.1016/j.cam.2009.05.015
关键词
Computational electromagnetism; Time-domain Maxwell's equations; Discontinuous Galerkin method; Explicit time integration; Non-conforming meshes
In this paper, we discuss the formulation, stability and validation of a high-order non-dissipative discontinuous Galerkin (DG) method for solving Maxwell's equations on non-conforming simplex meshes. The proposed method combines a centered approximation for the numerical fluxes at inter element boundaries, with either a second-order or a fourth-order leap-frog time integration scheme. Moreover, the interpolation degree is defined at the element level and the mesh is refined locally in a non-conforming way resulting in arbitrary-level hanging nodes. The method is proved to be stable and conserves a discrete counterpart of the electromagnetic energy for metallic cavities. Numerical experiments with high-order elements show the potential of the method. (C) 2009 Elsevier B.V. All rights reserved.
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