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Please use this identifier to cite or link to this item: http://ntour.ntou.edu.tw:8080/ir/handle/987654321/51860

Title: Applications of dual integral formulation in conjunction with fast mutipole method to oblique incident wave problem
Authors: K.H. Chen
J. T. Chen
J. H. Kao
Y. T.Lee
Contributors: 國立臺灣海洋大學:河海工程學系
Keywords: fast multipole method
oblique incident wave
thin barrier
modified Helmholtz equation
dual boundary element method
hypersingular equation
divergent series
Date: 2009-03
Issue Date: 2019-01-02T07:20:45Z
Publisher: International Journal for Numerical Methods in Fluids
Abstract: Abstract: In this paper, the dual integral formulation is derived for the modified Helmholtz equation in the propagation of oblique incident wave passing a thin barrier (zero thickness) by employing the concept of fast multipole method (FMM) to accelerate the construction of an influence matrix. By adopting the addition theorem, the four kernels in the dual formulation are expanded into degenerate kernels that separate the field point and the source point. The source point matrices decomposed in the four influence matrices are similar to each other or only to some combinations. There are many zeros or the same influence coefficients in the field point matrices decomposed in the four influence matrices, which can avoid calculating the same terms repeatedly. The separable technique reduces the number of floating‐point operations from O((N)2) to O(N loga(N)), where N is the number of elements and a is a small constant independent of N. Finally, the FMM is shown to reduce the CPU time and memory requirement, thus enabling us to apply boundary element method (BEM) to solve water scattering problems efficiently. Two‐moment FMM formulation was found to be sufficient for convergence in the singular equation. The results are compared well with those of conventional BEM and analytical solutions and show the accuracy and efficiency of the FMM. Copyright © 2008 John Wiley & Sons, Ltd.
Relation: 59(7) pp.711-751
URI: http://ntour.ntou.edu.tw:8080/ir/handle/987654321/51860
Appears in Collections:[河海工程學系] 期刊論文

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