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Locally Implicit Discontinuous Galerkin Methods for Time-Domain Maxwell's Equations

Ludovic Moya 1
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 : An attractive feature of discontinuous Galerkin (DG) spatial discretization is the possibility of using locally refined space grids to handle geometrical details. However, when combined with an explicit integration method to numerically solve a time-dependent partial differential equation, this readily leads to unduly large step size restrictions caused by the smallest grid elements. If the local refinement is strongly localized such that the ratio of fine to coarse elements is small, the unduly step size restrictions can be overcome by blending an implicit and an explicit scheme where only solution variables living at fine elements are implicitly treated. The counterpart of this approach is having to solve a linear system per time step. But due to the assumed small fine to coarse elements ratio, the overhead will also be small while the solution can be advanced in time with step sizes determined by the coarse elements. We propose to present two locally implicit methods for the time-domain Maxwell's equations. Our purpose is to compare the two with DG spatial discretization so that the most efficient one can be advocated for future use. Finally we will present a preliminary numerical investigation to increase the order of convergence.
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Submitted on : Thursday, January 30, 2014 - 4:13:05 PM
Last modification on : Monday, October 12, 2020 - 2:28:04 PM


  • HAL Id : hal-00939385, version 1



Ludovic Moya. Locally Implicit Discontinuous Galerkin Methods for Time-Domain Maxwell's Equations. ENUMATH 2011, the 9th European Conference on Numerical Mathematics and Advanced Applications, Sep 2011, Leicester, United Kingdom. pp.129-137. ⟨hal-00939385⟩



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