Conservative space-time mesh refinement methods for the FDTD solution of Maxwell’s equations |
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| Institution: | 1. CERFACS, Toulouse, France;2. E.D.F. Clamart, France;3. INRIA, Rocquencourt, Domaine de Voluceau, BP105, F-78153 Le Chesnay, Cedex, France;1. Department of Mathematics, Imperial College London, London SW7 2AZ, United Kingdom;2. Université de Toulouse; UPS, INSA, UT1, UTM, Institut de Mathématiques de Toulouse, CNRS, Institut de Mathématiques de Toulouse UMR 5219, F-31062 Toulouse, France;3. Université Paris-Est, Laboratoire d''Analyse et de Mathématiques Appliquées, (CNRS – UMR 8050), 5, boulevard Descartes, Cité Descartes – Champs-sur-Marne, F-77454 Marne-la-Vallée, France;1. School of Electronics Engineering, Kyungpook National University, 80 Daehakro, Bukgu, Daegu, 41566, Republic of Korea;2. Korea Institute of Industrial Technology (KITECH), 320 Techno-sunhwanro, Yuga-myeon, Dalseong-gun, Daegu, 42990, Republic of Korea;3. Department of Electrical Engineering, Gyeongsang National University, 501 Jinju-daero, Jinju-si, Gyeongsangnam-do, 52828, Republic of Korea;1. ElectroScience Laboratory and Department of Electrical and Computer Engineering, The Ohio State University, Columbus, OH 43212, USA;2. Trinum Research Inc., San Diego, CA 92126, USA;3. Intel Corporation, Hillsboro, OR 97124, USA;4. Department of Electrical and Computer Engineering, University of Sao Paulo, Sao Carlos, SP 13566-590, Brazil;1. Department of Physics, University of Illinois at Urbana-Champaign, IL, USA;2. Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, IL, USA;1. Institute for Computational Engineering and Sciences (ICES), Department of Aerospace Engineering and Engineering Mechanics, University of Texas at Austin, Austin, TX 78712, United States;2. Institute for Fusion Studies (IFS), Department of Physics, University of Texas at Austin, Austin, TX 78712, United States;3. Institute for Computational Engineering and Sciences (ICES), University of Texas at Austin, Austin, TX 78712, United States |
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| 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. |
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