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Boundary Element Analysis pp 113–134Cite as

Sparse Convolution Quadrature for Time Domain Boundary Integral Formulations of the Wave Equation by Cutoff and Panel-Clustering

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Part of the Lecture Notes in Applied and Computational Mechanics book series (LNACM,volume 29)

Abstract

We consider the wave equation in a time domain boundary integral formulation. To obtain a stable time discretization, we employ the convolution quadrature method in time, developed by Lubich. In space, a Galerkin boundary element method is considered. The resulting Galerkin matrices are fully populated and the computational complexity is proportional to N log2 NM 2, where M is the number of spatial unknowns and N is the number of time steps.

We present two ways of reducing these costs. The first is an a priori cutoff strategy, which allows to replace a substantial part of the matrices by 0. The second is a panel clustering approximation, which further reduces the storage and computational cost by approximating subblocks by low rank matrices.

Keywords

  • Boundary Element Method
  • Convolution Quadrature
  • Versus B95L
  • Galerkin Boundary Element Method
  • Convolution Quadrature Method

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Author information

Authors and Affiliations

  1. Max-Planck-Institut für Mathematik in den Naturwissenschaften, Inselstrasse 20-26, 04103, Leipzig, Germany

    Wolfgang Hackbusch & Wendy Kress

  2. Institut für Mathematik, Universität Zürich, Winterthurerstrasse 190, 8057, Zürich, Switzerland

    Stefan A. Sauter

Authors
  1. Wolfgang Hackbusch
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  2. Wendy Kress
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  3. Stefan A. Sauter
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Editor information

Editors and Affiliations

  1. Institut für Baumechanik, Technische Universität Graz, Technikerstr. 4, 8010, Graz, Austria

    Prof. Dr.-Ing. Martin Schanz

  2. Institut für Numerische Mathematik, Technische Universität Graz, Steyrergasse 30, 8010, Graz, Austria

    Prof. Dr. Olaf Steinbach

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Hackbusch, W., Kress, W., Sauter, S.A. (2007). Sparse Convolution Quadrature for Time Domain Boundary Integral Formulations of the Wave Equation by Cutoff and Panel-Clustering. In: Schanz, M., Steinbach, O. (eds) Boundary Element Analysis. Lecture Notes in Applied and Computational Mechanics, vol 29. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-47533-0_5

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