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Numerical Stability of Collocation Schemes for Time Domain Boundary Integral Equations

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Computational Electromagnetics

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 28))

Summary

Time domain boundary integral formulations of transient scattering problems involve retarded potential integral equations (RPIEs). Collocation schemes for RPIEs are often unstable, having errors which oscillate and grow exponentially with time. We describe how Fourier analysis can be used to analyse the stability of uniform grid schemes and to show that the instabilities are often very different from those observed in PDE approximations. We also present a new stable collocation scheme for a scalar RPIE, and show that it converges.

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Author information

Authors and Affiliations

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

    Penny Davies

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

    Dugald Duncan

Authors
  1. Penny Davies
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  2. Dugald Duncan
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Editor information

Editors and Affiliations

  1. Department of Mathematical Sciences, University of Delaware, Newark, DE, 19717, USA

    Peter Monk

  2. Institute for Applied Mathematics, Vienna University of Technology, Wiedner Hauptstraße 8-10, 1040, Vienna, Austria

    Carsten Carstensen

  3. Institute of Mathematics, University of Erlangen-Nürnberg, Bismarckstraße 1 1/2, 91054, Erlangen, Germany

    Stefan Funken

  4. Max-Planck-Institute for Mathematics in the Sciences, Inselstraße 22, 04103, Liepzig, Germany

    Wolfgang Hackbusch

  5. Department of Mathematics, University of Augsburg, Universitätsstraße 14, 86159, Augsburg, Germany

    Ronald H. W. Hoppe

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© 2003 Springer-Verlag Berlin Heidelberg

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Davies, P., Duncan, D. (2003). Numerical Stability of Collocation Schemes for Time Domain Boundary Integral Equations. In: Monk, P., Carstensen, C., Funken, S., Hackbusch, W., Hoppe, R.H.W. (eds) Computational Electromagnetics. Lecture Notes in Computational Science and Engineering, vol 28. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-55745-3_5

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  • DOI: https://doi.org/10.1007/978-3-642-55745-3_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-44392-6

  • Online ISBN: 978-3-642-55745-3

  • eBook Packages: Springer Book Archive

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