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 will present the panel clustering algorithm which avoids the generation of the N 2 matrix entries by representing the integral operator on the discrete level by only О (N logk N) quantities. Thus, a matrix vector multiplication as a basic step in every iterative solver can be performed by О(N logk N) operations. This method can be applied to all kinds of integral equations discretized by, e.g., the Nyström, the collocation or the Galerkin method.
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Sauter, S.A. (1998). The panel clustering method in 3-d bem. In: Papanicolaou, G. (eds) Wave Propagation in Complex Media. The IMA Volumes in Mathematics and its Applications, vol 96. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1678-0_10
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