Treatment of rank deficiency in acoustics using SVD

被引：36

作者：

Chen, J. T. ^{[1
]}

Chen, I. L.

Chen, K. H.

机构：

[1] Natl Taiwan Ocean Univ, Dept Harbor & River Engn, Chilung 2024, Taiwan

[2] Natl Kaohsiung Marine Univ, Dept Naval Architecture, Kaohsiung, Taiwan

[3] Toko Univ, Dept Informat Management, Chiayi, Taiwan

来源：

JOURNAL OF COMPUTATIONAL ACOUSTICS | 2006年 / 14卷 / 02期

关键词：

rank deficiency; circulant; degenerate kernel; BEM; spurious eigenvalue; fictitious frequency;

D O I：

10.1142/S0218396X06002998

中图分类号：

O42 [声学];

学科分类号：

070206 ; 082403 ;

摘要：

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.

引用

页码：157 / 183

页数：27

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