Numerische Mathematik

, Volume 95, Issue 2, pp 223–251 | Cite as

A Conservative Space-time Mesh Refinement Method for the 1-D Wave Equation. Part II: Analysis



We introduced in [2] a new method for space-time refinement for the 1-D wave equation. This method is based on the conservation of a discrete energy through two different discretization grids which guarantees the stability of the scheme. In this second part, we analyse the accuracy of this scheme in a detailed way by means of a plane wave analysis and numerical experiments that permit us to point out spurious numerical phenomena and explain how to control them.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Chevalier, M.W., Luebbers, R.J.: FDTD Local Grid with Material Traverse. IEEE Trans. Antennas and Propagation 45(3), 411–421 (1997)CrossRefGoogle Scholar
  2. 2.
    Collino, F., Fouquet, T., Joly, P.: A conservative space-time mesh refinement method for the 1-d wave equations: Construction. Numer. Math. 95(2), 197–221 (2003)Google Scholar
  3. 3.
    Elliot, D.F., Ramamohan rao, K.: Fast Transforms Algorithms Analyses Applications., volume H-19. Academic Press NY, London, 1982Google Scholar
  4. 4.
    Fouquet, T.: Raffinement de maillage spatio temporel pour les équations de Maxwell. Université Paris IX Dauphine, June 2000Google Scholar
  5. 5.
    Kim, I.S., Hoefer, W.J.R.: A local mesh refinement algorithm for the time-domain finite-difference method to solve Maxwell's equations. IEEE Trans. Microwave Theory Tech. 38(6), 812–815 (1990)Google Scholar
  6. 6.
    Kunz, K.S., Simpson, L.: A technique for increasing the resolution of finite-difference solutions to the Maxwell equations. IEEE Trans. Electromagn. Compat. EMC-23, 419–422 (1981)Google Scholar
  7. 7.
    Prescott, D.T., Shuley, N.V.: A method for incorporating different sized cells into the finite-difference time-domain analysis technique. IEEE Microwave Guided Wave Lett. 2, 434–436 (1992)CrossRefGoogle Scholar
  8. 8.
    Collino, F., Fouquet, T., Joly, P.: Analyse numérique d'une méthode de raffinement demaillage espace-temps pour l'équation des ondes. INRIA, 3474 1998Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  1. 1.INRIA Rocquencourt BP105 Le ChesnayFrance

Personalised recommendations