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Journal of Scientific Computing

, Volume 56, Issue 1, pp 190–218 | Cite as

Locally Implicit Time Integration Strategies in a Discontinuous Galerkin Method for Maxwell’s Equations

  • Stéphane Descombes
  • Stéphane Lanteri
  • Ludovic Moya
Article

Abstract

An attractive feature of discontinuous Galerkin (DG) spatial discretization is the possibility of using locally refined space grids to handle geometrical details. However, locally refined meshes lead to severe stability constraints on explicit integration methods to numerically solve a time-dependent partial differential equation. If the region of refinement is small relative to the computational domain, the time step size restriction can be overcome by blending an implicit and an explicit scheme where only the solution variables living at fine elements are treated implicitly. The downside of this approach is having to solve a linear system per time step. But due to the assumed small region of refinement relative to the computational domain, the overhead will also be small while the solution can be advanced in time with step sizes determined by the coarse elements. In this paper, we present two locally implicit time integration methods for solving the time-domain Maxwell equations spatially discretized with a DG method. Numerical experiments for two-dimensional problems illustrate the theory and the usefulness of the implicit–explicit approaches in presence of local refinements.

Keywords

Discontinuous Galerkin spatial discretization  Locally implicit time integration methods Time-domain Maxwell equations 

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Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  • Stéphane Descombes
    • 1
  • Stéphane Lanteri
    • 2
  • Ludovic Moya
    • 2
  1. 1.J.A. Dieudonné Mathematics Laboratory, CNRS UMR 7351University Nice Sophia AntipolisNice CedexFrance
  2. 2.Inria Sophia Antipolis—Méditerranée, Nachos project-team 2004 Route des LuciolesSophia Antipolis CedexFrance

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