Conservative space-time mesh refinement methods for the FDTD solution of Maxwell's equations

Francis Collino 1 Thierry Fouquet 1 Patrick Joly 1
1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
Inria Saclay - Ile de France, ENSTA ParisTech UMA - Unité de Mathématiques Appliquées, CNRS - Centre National de la Recherche Scientifique : UMR7231
Abstract : A new variational space-time mesh refinement method is proposed for the FDTD solution of Maxwell's equations. The main advantage of this method is to guarantee the conservation of a discrete energy that implies that the scheme remains L2 stable under the usual CFL condition. The only additional cost induced by the mesh refinement is the inversion, at each time step, of a sparse symmetric positive definite linear system restricted to the unknowns located on the interface between coarse and fine grid. The method is presented in a rather general way and its stability is analyzed. An implementation is proposed for the Yee scheme. In this case, various numerical results in 3-D are presented in order to validate the approach and illustrate the practical interest of space-time mesh refinement methods.
Type de document :
Article dans une revue
Journal of Computational Physics, Elsevier, 2006, 211 (1), pp.9-35. <10.1016/j.jcp.2005.03.035>
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Contributeur : Aurélien Arnoux <>
Soumis le : vendredi 11 avril 2014 - 14:58:57
Dernière modification le : jeudi 9 février 2017 - 15:28:13

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Francis Collino, Thierry Fouquet, Patrick Joly. Conservative space-time mesh refinement methods for the FDTD solution of Maxwell's equations. Journal of Computational Physics, Elsevier, 2006, 211 (1), pp.9-35. <10.1016/j.jcp.2005.03.035>. <hal-00977715>

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