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    Item type:Publication, Access status: without files ,
    hp Fast multipole boundary element method for 3D acoustics
    (2017-06-01)
    Keuchel, Sören
    ;
    Vater, Kerstin
    ;
    Estorff, Otto von
    A fast multipole boundary element method (FMBEM) extended by an adaptive mesh refinement algorithm for solving acoustic problems in three-dimensional space is presented in this paper. The Collocation method is used, and the Burton–Miller formulation is employed to overcome the fictitious eigenfrequencies arising for exterior domain problems. Because of the application of the combined integral equation, the developed FMBEM is feasible for all positive wave numbers even up to high frequencies. In order to evaluate the hypersingular integral resulting from the Burton–Miller formulation of the boundary integral equation, an integration technique for arbitrary element order is applied. The fast multipole method combined with an arbitrary order h-p mesh refinement strategy enables accurate computation of large-scale systems. Numerical examples substantiate the high accuracy attainable by the developed FMBEM, while requiring only moderate computational effort at the same time.
    Publicationtype: Journal Article
      133
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    Item type:Publication, Access status: without files ,
    A high order fast multipole boundary element method
    (2015-07)
    Keuchel, Sören
    ;
    Vater, Kerstin
    ;
    Estorff, Otto von
    The Boundary Element Method can be used to solve the Helmholtz equation in three dimensions. Just the surface has to be discretized, but a solution for the complete domain is obtained. Especially for exterior domains this is an enormous advantage. A drawback of the solution procedure, however is its quadratic complexity. The Fast Multipole Method results in a quasi linear complexity due to an approximation of a matrix vector product and is therefore applicable for solving large scale systems. The variables on the surface are approximated by ansatz functions of a certain order. Typically constant, linear or quadratic element orders are used. In this contribution formulations for arbitrary ansatz functions are presented. Since an application to exterior cases leads to the problem of fictitious frequencies, a Burton Miller formulation is embedded. The presented Collocation Method can treat the hypersingular kernels for arbitrary ansatz functions correctly. The theoretical background is introduced and numerical examples show the performance of the formulation.
    Publicationtype: Conference Paper
      41