95-4   Berichtsreihe des Mathematischen Seminars der Universität Kiel

Wolfgang Hackbusch, Christian Lage, Stefan A. Sauter:

On the Efficient Realization of Sparse Matrix Techniques for Integral Equations with Focus on Panel Clustering, Cubature and Software Design Aspects

The method of integral equations is an elegant tool where boundary value problems on a domain \Omega are transformed into integral equations defined on the surface of \Omega. The discretization via the boundary element method (BEM) has several advantages compared to FE-discretizations of PDEs on the whole domain \Omega. On the other hand, the most significant drawback of the BEM is that the system matrix is full and, in addition, the computation of the elements requires the evaluation of complicated surface integrals. In this paper we show how to avoid the generation of the whole system matrix by means of the panel clustering method which represents the discrete operator in an alternative form. Only matrix elements close to the diagonal have to be computed. Furthermore, we will present new semi-analytic techniques for computing those nearfield matrix entries efficiently.
From the view point of software design aspects the efficient realization of boundary elements, especially the panel clustering algorithm, is a non-trivial task. We will explain how the complexity of implementing the multifarious BEM can be managed by object-oriented design methods.

Bibliographical note: In: Wendland, W. (Hrsg.), Boundary Element Topics, 51-76, Springer (1997).


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