The paper is organized as follows. In the next section, we go briefly through the setting of Petrov-Galerkin discretization of boundary integral equations and introduce the notations necessary for the sequel. Then, in Section 3, we investigate the computation of the surface integrals arising when computing the matrix entries of the linear system. First, we have to provide some analytical properties of the kernel functions that arise, which then are used in the design of efficient cubature strategies. (Note that in more than one dimension the term quadrature is replaced by cubature). In Section 4, we explain the panel clustering algorithm. After having developed the basic principle, we formulate the algorithm and present an error analysis. Estimates of the asymptotic complexity of the algorithm follow and remarks on their relevance for practical problem sizes are given. Section 6 is devoted to the design of modern BEM software in C++. It is explained which data structures are well suited to making the different algorithms efficient and flexible with respect to various kinds of integral equations, discretization schemes such as, e.g., collocation or Galerkin BEMs, and various geometries and cubature techniques.

Hackbusch, W; Lage, C; Sauter, S (1997). *On the efficient realization of sparse matrix techniques for integral equations with focus on panel clustering, cubature and software design aspects.* In: Wendland, W. Boundary element topics (Stuttgart, 1995). Berlin: Springer, 51-75.

## Abstract

The paper is organized as follows. In the next section, we go briefly through the setting of Petrov-Galerkin discretization of boundary integral equations and introduce the notations necessary for the sequel. Then, in Section 3, we investigate the computation of the surface integrals arising when computing the matrix entries of the linear system. First, we have to provide some analytical properties of the kernel functions that arise, which then are used in the design of efficient cubature strategies. (Note that in more than one dimension the term quadrature is replaced by cubature). In Section 4, we explain the panel clustering algorithm. After having developed the basic principle, we formulate the algorithm and present an error analysis. Estimates of the asymptotic complexity of the algorithm follow and remarks on their relevance for practical problem sizes are given. Section 6 is devoted to the design of modern BEM software in C++. It is explained which data structures are well suited to making the different algorithms efficient and flexible with respect to various kinds of integral equations, discretization schemes such as, e.g., collocation or Galerkin BEMs, and various geometries and cubature techniques.

## Citations

## Additional indexing

Other titles: | Proceedings of the final conference of the Priority Research Programme "Boundary Element Methods 1989–1995'' of the German Research Foundation held in Stuttgart, October 2–4, 1995 |
---|---|

Item Type: | Book Section, refereed, original work |

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

Dewey Decimal Classification: | 510 Mathematics |

Language: | English |

Date: | 1997 |

Deposited On: | 29 Nov 2010 16:28 |

Last Modified: | 05 Apr 2016 13:26 |

Publisher: | Springer |

ISBN: | 3-540-62850-9 |

Related URLs: | http://www.zentralblatt-math.org/zbmath/search/?q=an%3A0884.65114 |

## Download

Full text not available from this repository.

TrendTerms displays relevant terms of the abstract of this publication and related documents on a map. The terms and their relations were extracted from ZORA using word statistics. Their timelines are taken from ZORA as well. The bubble size of a term is proportional to the number of documents where the term occurs. Red, orange, yellow and green colors are used for terms that occur in the current document; red indicates high interlinkedness of a term with other terms, orange, yellow and green decreasing interlinkedness. Blue is used for terms that have a relation with the terms in this document, but occur in other documents.

You can navigate and zoom the map. Mouse-hovering a term displays its timeline, clicking it yields the associated documents.