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Please use this identifier to cite or link to this item: http://ntour.ntou.edu.tw:8080/ir/handle/987654321/24400

Title: Treatment of rank deficiency in acoustics using SVD
Authors: J. T. CHEN;I. L. CHEN;K. H. CHEN
Contributors: NTOU:Department of Harbor and River Engineering
Keywords: Rank deficiency;circulant;degenerate kernel;BEM;spurious eigenvalue;fictitious frequency
Date: 2006
Issue Date: 2011-10-20T08:12:11Z
Publisher: Journal of Computational Acoustics
Abstract: abstract:In this paper, we proposed a unified formulation to explain the reason why spurious eigensolution occurs in the eigenproblem of interior acoustics using the real-part and imaginary-part BEMs and why fictitious frequency occurs in exterior acoustics using the complex-valued BEM. Both the two problems stem from the rank deficiency of the influence matrix. Based on the circulant properties and degenerate kernels, an analytical study in a discrete system for a circular cavity is conducted. The Fredholm alternative theorem is employed to study the rank-deficiency problems in conjunction with singular value decomposition updating technique. The spurious and fictitious boundary modes are found to locate in the column vectors of left unitary matrix. Also, the effects of different types of boundary condition on the spurious and fictitious solutions using direct and indirect methods are discussed. The mathematical and physical meanings for the nontrivial boundary solution in spurious eigensolution and fictitious frequency are explained. Numerical experiments are found to agree with the analytical predictions.
Relation: 14(2), pp.157-183
URI: http://ntour.ntou.edu.tw/handle/987654321/24400
Appears in Collections:[河海工程學系] 期刊論文

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