Abstract
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.
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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)
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)
Ostermann, E.: PhD thesis, Institut für Angewandte Mathematik, Leibniz Universität Hannover (in preparation)
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Stephan, E.P., Maischak, M., Ostermann, E. (2008). Transient Boundary Element Method and Numerical Evaluation of Retarded Potentials. In: Bubak, M., van Albada, G.D., Dongarra, J., Sloot, P.M.A. (eds) Computational Science – ICCS 2008. ICCS 2008. Lecture Notes in Computer Science, vol 5102. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69387-1_35
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DOI: https://doi.org/10.1007/978-3-540-69387-1_35
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-69386-4
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