Transient Boundary Element Method and Numerical Evaluation of Retarded Potentials

  • Ernst P. Stephan
  • Matthias Maischak
  • Elke Ostermann
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5102)


We discuss the modeling of transient wave propagation with the boundary element method (BEM) in three dimensions. The special structure of the fundamental solution of the wave equation leads to a close interaction of space and time variables in a so-called retarded time-argument. We give a detailed derivation of the discretization scheme and analyse a new kind of ”geometrical light cone” singularity of the retarded potential function. Moreover, we present numerical experiments that show these singularities.


retarded potential transient boundary element method 


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    Ha-Duong, T.: On retarded potential boundary integral equations and their discretisation. In: Topics in computational wave propagation. Lect. Notes Comput. Sci. Eng, vol. 31, pp. 301–336. Springer, Berlin (2003)Google Scholar
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    Maischak, M., Ostermann, E., Stephan, E.P.: On the numerical evaluation of retarded potentials. Institut für Angewandte Mathematik, Leibniz Universität Hannover, Preprint no. 89 (2007)Google Scholar
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    Ostermann, E.: PhD thesis, Institut für Angewandte Mathematik, Leibniz Universität Hannover (in preparation)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Ernst P. Stephan
    • 1
  • Matthias Maischak
    • 2
  • Elke Ostermann
    • 1
  1. 1.Institut für Angewandte MathematikLeibniz Universität HannoverHannoverGermany
  2. 2.School of Information Systems, Computing & MathematicsBrunel UniversityUxbridgeUnited Kingdom

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