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Please use this identifier to cite or link to this item: http://ntour.ntou.edu.tw:8080/ir/handle/987654321/24605

Title: Boundary element analysis for the Helmholtz eigenvalue problems with a multiply connected domain
Authors: 陳正宗;林建華;郭世榮;全湘偉
J. T. Chen;J. H. Lin;S. R. Kuo;S. W. Chyuan
Contributors: NTOU:Department of Harbor and River Engineering
國立臺灣海洋大學:河海工程學系
Keywords: boundary elements;spurious eigenvalue;degenerate kernel;circulant multiply connected problem;burton-miller method
Date: 2001-10-08
Issue Date: 2011-10-20T08:13:07Z
Publisher: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Abstract: Abstract:For a Helmholtz eigenvalue problem with a multiply connected domain, the boundary integral equation approach as well as the boundary-element method is shown to yield spurious eigenvalues. even if the complex-valued kernel is used. In such a case, it is found that spurious eigenvalues depend on the geometry of the inner boundary. Demonstrated as an analytical case, the spurious eigenvalue for a multiply connected problem with its inner boundary as a circle is studied analytically. By using the degenerate kernels and circulants, an annular case can be studied analytically in a discrete system and can be treated as a special case. The proof for the general boundary instead of the circular boundary is also derived. The Burton-Miner method is employed to eliminate spurious eigenvalues in the multiply connected case. Moreover, a modified method considering only the real-part formulation is provided. Five examples are shown to demonstrate that the spurious eigenvalues depend on the shape of the inner boundary. Good agreement between analytical prediction and numerical results are found.
Relation: 457(2014), pp.2521-2546
URI: http://ntour.ntou.edu.tw/handle/987654321/24605
Appears in Collections:[河海工程學系] 期刊論文

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