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Topics in Computational Wave Propagation pp 301–336Cite as

On Retarded Potential Boundary Integral Equations and their Discretisation

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Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 31))

Summary

The paper deals with the retarded potential boundary integral equations (RPBIE) used in the numerical resolution of transient scattering problems (the so-called time domain boundary element methods). We propose here a review and update of the mathematical analysis of the involved RPBIE. Our approach, via Laplace transform, is described in some details for the classical acoustic scattering problems. The main results are: (i) existence and uniqueness theorems on a functional framework closely linked to the energy of the scattered waves; (ii) space-time variational formulations for the so-called “first kind” RPBIE, with coerciveness obtained by energy estimates. That leads us to advocate choosing these first kind RPBIE and their Galerkin approximations, instead of the second kind RPBIE and the collocation approximations. The actual space-time boundary elements are described in some detail. Examples of numerical experiments that confirm the unconditional stability of our schemes are reported, as well as references for similar results in other related work.

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Authors and Affiliations

  1. Université de Technologie de Compiègne, BP 20529, 60205, Compiègne Cedex, France

    Tuong Ha-Duong

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  1. Tuong Ha-Duong
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Editors and Affiliations

  1. Department of Mathematics, University of Strathclyde, Richmond Street 26, Glasgow, G1 1XH, UK

    Mark Ainsworth  & Penny Davies  & 

  2. Department of Mathematics, Heriot-Watt University, Riccarton Campus, EH14 4AS, Edinburgh, UK

    Dugald Duncan  & Bryan Rynne  & 

  3. Department of Mathematics and Computer Sciences, Colorado School of Mines, 80401-1887, Golden, USA

    Paul Martin

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Ha-Duong, T. (2003). On Retarded Potential Boundary Integral Equations and their Discretisation. In: Ainsworth, M., Davies, P., Duncan, D., Rynne, B., Martin, P. (eds) Topics in Computational Wave Propagation. Lecture Notes in Computational Science and Engineering, vol 31. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-55483-4_8

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  • DOI: https://doi.org/10.1007/978-3-642-55483-4_8

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