G. Variational FDTD-like Methods for Maxwell’s Equations

  • Patrick Joly
Conference paper
Part of the Mathematics in Industry book series (MATHINDUSTRY, volume 4)


In this article, we describe two types of conservative variational techniques that aim at improving the use of FDTD methods for the treatment of complex geometries with time dependent Maxwell’s equations.


Coarse Grid Fine Grid Mixed Finite Element FDTD Method Fictitious Domain 
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  1. 1.
    A. Bendali. Approximation par éléments finis de surface de problèmes de diffraction des ondes électromagnétiques. PhD thesis, Université Paris VI, 1984.Google Scholar
  2. 2.
    F. Brezzi and M. Fortin. Mixed and Hybrid Finite Element Methods. Springer Series in Computational Mathematics (15). Springer Verlag, 1991.Google Scholar
  3. 3.
    A. Buffa and P. Ciarlet Jr. On traces for functional spaces related to Maxwell’s equations. I. an integration by parts formula in Lipschitz polyhedra. Mathematical Methods in the Applied Sciences, 24(1):9–30, 2001.MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    M. Clemens, P. Thoma, T. Weiland, and U. van Rienen. Computational electromagnetic-field calculation with the finite-integration method. Surveys Math. Indust., 8(3-4):213–232, 1999.MathSciNetzbMATHGoogle Scholar
  5. 5.
    F. Collino, P. Joly, and F. Millot. Fictitious domain method for unsteady problems: Application to electromagnetic scattering. Journal of Corny. Physics, 138:907–938, 1997.MathSciNetzbMATHGoogle Scholar
  6. 6.
    B. Engquist and A. Majda. Absorbing boundary conditions for the numerical simulation of waves. Math. of Comp., 31:629–651, 1977.MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    S. Garcés. Application des méthodes de domaines fictifs à la modélisation des structures rayonnantes tridimensionnelles Etude mathématique et numérique d’un modèle. PhD thesis, ENSAE (Toulouse), 1997.Google Scholar
  8. 8.
    V. Girault and R. Glowinski. Error analysis of a fict. domain method applied to a Dirichlet problem. Japan J. Ind. Appl. Math., 12(3):487–514, 1995.MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    P. Joly and L. Rhaouti. Domaines fictifs, éléments finis h(div) et condition de neumann: le problème de la condition inf-sup. C. R. Acad. Sci. Paris, Série I, 328:1225–1230, 1999.MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    J.C. Nedelec. Mixed finite elements in R3. Num. Math., 35:315–341, 1980.MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    S. Piperno, M. Remaki, and L. Fezoui. A nondiffusive finite volume scheme for the three-dimensional Maxwell’s equations on unstructured meshes. SIAM J. Numer. Anal., 9(6):2089–2108, 2002.MathSciNetCrossRefGoogle Scholar
  12. 12.
    A. Taflove. Computational Electrodynamics, The Finite-Difference Time Domain method. Artech House, London, 1995.zbMATHGoogle Scholar
  13. 13.
    K.S. Yee. Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media. IEEE Trans, on Antennas and propagation, pages 302–307, 1966.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Patrick Joly
    • 1
  1. 1.INRIA RocquencourtLe ChesnayFrance

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