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.

Hackbusch, W; Kress, W; Sauter, S (2007). *Sparse convolution quadrature for time domain boundary integral formulations of the wave equation by cutoff and panel-clustering.* In: Schanz, M; Steinbach, O. Boundary element analysis. Berlin: Springer, 113-134.

## 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.

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## Additional indexing

Item Type: | Book Section, refereed, original work |
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Communities & Collections: | 07 Faculty of Science > Institute of Mathematics |

Dewey Decimal Classification: | 510 Mathematics |

Language: | English |

Date: | 2007 |

Deposited On: | 11 Dec 2009 07:50 |

Last Modified: | 05 Apr 2016 13:23 |

Publisher: | Springer |

Series Name: | Lecture Notes in Applied and Computational Mechanics |

Number: | 29 |

ISBN: | 978-3-540-47465-4 |

Publisher DOI: | https://doi.org/10.1007/978-3-540-47533-0 |

Related URLs: | http://www.ams.org/mathscinet-getitem?mr=2307201 |

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