In many cases, boundary value problems on a domain Ω can be rewritten as integral equations on the boundary of Ω. The discretization of this integral equation leads to a system of linear equations with a dense coefficient matrix of dimension N. In this paper, we present a panel clustering algorithm which avoids the generation of the N2 matrix entries by representing the integral operator on the discrete level by only O(NlogκN) quantities. Thus, a matrix vector multiplication as a basis step in every iterative solver can be performed by O(NlogκN) operations. This method can be applied to all kinds of integral equations discretized by, e.g., the Nyström, the collocation or the Galerkin method.

Sauter, S (1998). *The panel clustering method in 3-D BEM.* In: Papanicolaou, G. Wave propagation in complex media (Minneapolis, MN, 1994). New York: Springer, 199-224.

## Abstract

In many cases, boundary value problems on a domain Ω can be rewritten as integral equations on the boundary of Ω. The discretization of this integral equation leads to a system of linear equations with a dense coefficient matrix of dimension N. In this paper, we present a panel clustering algorithm which avoids the generation of the N2 matrix entries by representing the integral operator on the discrete level by only O(NlogκN) quantities. Thus, a matrix vector multiplication as a basis step in every iterative solver can be performed by O(NlogκN) operations. This method can be applied to all kinds of integral equations discretized by, e.g., the Nyström, the collocation or the Galerkin method.

## Citations

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## Additional indexing

Other titles: | Proceedings of the IMA Workshops on Wavelets, Multigrid and Other Fast Algorithms (Multiple, FFT) and Their Use in Wave Propagation and Waves in Random and Other Complex Media held at the University of Minnesota, Minneapolis, MN, 1994. |
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Item Type: | Book Section, refereed, original work |

Communities & Collections: | 07 Faculty of Science > Institute of Mathematics |

Dewey Decimal Classification: | 510 Mathematics |

Language: | English |

Date: | 1998 |

Deposited On: | 29 Nov 2010 16:28 |

Last Modified: | 14 Sep 2016 13:39 |

Publisher: | Springer |

Series Name: | The IMA Volumes in Mathematics and its Applications |

Number: | 96 |

ISSN: | 0940-6573 |

ISBN: | 0-387-98309-0 |

Related URLs: | http://www.zentralblatt-math.org/zbmath/search/?q=an%3A0901.65070 http://www.springer.com/mathematics/analysis/book/978-0-387-98309-7 http://www.recherche-portal.ch/primo_library/libweb/action/search.do?fn=search&mode=Advanced&vid=ZAD&vl%28186672378UI0%29=isbn&vl%281UI0%29=contains&vl%28freeText0%29=0-387-98309-0 |

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