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3D Maxwell's equations and orthogonal nonconforming meshes: a hp-type Discontinuous Galerkin method

Nicolas Canouet 1 Loula Fezoui 1 Serge Piperno 1
1 CAIMAN - Scientific computing, modeling and numerical analysis
CRISAM - Inria Sophia Antipolis - Méditerranée , ENPC - École des Ponts ParisTech, CNRS - Centre National de la Recherche Scientifique : UMR6621
Abstract : We present a Discontinuous Galerkin scheme to solve the time-domain Maxwell's equations on conforming or nonconforming orthogonal grids. The method relies on a set of local basis functions whose degree may vary at subgrid interfaces. We also choose a centered mean approximation for the surface integrals and a second-order leap-frog scheme for advancing in time. We prove that the resulting scheme is stable and that it conserves a discrete analog of the electromagnetic energy. We also analyse the dispersion error in the uniform mesh case.
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https://hal.inria.fr/inria-00071668
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Submitted on : Tuesday, May 23, 2006 - 6:27:35 PM
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Nicolas Canouet, Loula Fezoui, Serge Piperno. 3D Maxwell's equations and orthogonal nonconforming meshes: a hp-type Discontinuous Galerkin method. [Research Report] RR-4912, INRIA. 2003. ⟨inria-00071668⟩

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