High-order time integration Leap-Frog schemes combined with a discontinuous Galerkin method for the solution of the Maxwell equations

Dmitry V. Ponomarev 1, *
* Corresponding author
1 NACHOS - Numerical modeling and high performance computing for evolution problems in complex domains and heterogeneous media
CRISAM - Inria Sophia Antipolis - Méditerranée , JAD - Laboratoire Jean Alexandre Dieudonné : UMR6621
Abstract : In this report, after pedagogical mathematical insight into basic notions of numerical analysis for differential equations, more specific Discontinuous Galerkin (DG) method is introduced. Afterwards, the DG method is combined with a fourth-order staggered Leap-Frog (LF4) scheme to be applied to the solution of the Maxwell equations wave-propagation problem. Stability analysis of the resulting scheme is performed and some peculiarities related with the choice of basis functions in the DG method are stressed.
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Dmitry V. Ponomarev. High-order time integration Leap-Frog schemes combined with a discontinuous Galerkin method for the solution of the Maxwell equations. [Research Report] RR-7067, INRIA. 2009, pp.91. ⟨inria-00424560⟩

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