Numerical experiments for acoustic modes of a square cavity using the dual boundary element method

Chen, J.T.; Chen, K.H.; Chyuan, Shiang-Woei

doi:10.1016/s0003-682x(98)00062-0

Cited by 32 publications

(20 citation statements)

References 23 publications

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“…This is the reason why the one mode can be rotated to another mode. A similar explanation can also be found in Reference [26]. It is also found that the result of case 2 in Figure 2(f) does not match the analytical solution very well.…”

Section: Filtering Out the Spurious Eigensolutions By Using Svd Updatsupporting

confidence: 86%

The Boundary Collocation Method With Meshless Concept for Acoustic Eigenanalysis of Two-Dimensional Cavities Using Radial Basis Function

Chen¹,

Chang²,

Chen³

et al. 2002

Journal of Sound and Vibration

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In this paper, a meshless method for the acoustic eigenfrequencies using radial basis function (RBF) is proposed. The coefficients of influence matrices are easily determined by the two-point functions. In determining the diagonal elements of the influence matrices, two techniques, limiting approach and invariant method, are employed. Based on the RBF in the imaginary-part kernel, the method results in spurious eigenvalues which can be separated by using the singular value decomposition (SVD) technique in conjunction with the Fredholm alternative theorem. To understand why the spurious eigenvalues occur, analytical study in the discrete system by discretizing the circular boundary is conducted by using circulants. By using the SVD updating terms and documents, the true and spurious eigensolutions can be extracted out respectively. Several examples are demonstrated to see the validity of the present method. #

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Section: Filtering Out the Spurious Eigensolutions By Using Svd Updatsupporting

confidence: 86%

The Boundary Collocation Method With Meshless Concept for Acoustic Eigenanalysis of Two-Dimensional Cavities Using Radial Basis Function

Chen¹,

Chang²,

Chen³

et al. 2002

Journal of Sound and Vibration

Self Cite

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“…To solve this equation using the BEM, the complex-valued kernels are usually adopted, and the following equation can be derived [29]:…”

Section: Construction Of Various Bem Formulationsmentioning

confidence: 99%

Applications of the Generalized Singular-Value Decomposition Method on the Eigenproblem Using the Incomplete Boundary Element Formulation

Kuo

Yeih

2000

Journal of Sound and Vibration

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In this paper, four incomplete boundary element formulations, including the real-part singular boundary element, the real-part hypersingular boundary element, the imaginary-part boundary element and the plane-wave element methods, are used to solve the free vibration problem. Among these incomplete boundary element formulations, the real-part singular and the hypersingular boundary elements are of the singular type and the other two are of the regular type. When the incomplete formulation is used, the spurious eigensolution may be encountered. An auxiliary system, whose boundary conditions are linearly independent of those of the original system, is required in the proposed method in order to eliminate the spurious eigensolution. A mathematical proof is given to show that the spurious eigensolution will appear in both the original and auxiliary systems. As a result, one can eliminate spurious eigensolution by means of the generalized singular-value decomposition method. In addition to the spurious eigensolution problem, the regular boundary element formulation further su!ers ill-conditioned behaviors in the problem solver. It is explained analytically using a circular domain why ill-conditioned behaviors exist. Two main ill-conditioned problems are the numerical instability of solution and the nonexistence of solution. To solve the numerical instability of solution problem existing in these proposed regular formulations, the Tikhonov's regularization technique is used to improve the condition number of the leading coe$cient matrix; further, the generalized singular-value decomposition method is used to eliminate spurious eigensolutions. Numerical examples are given to verify the performance of these proposed methods, and the results match the analytical values well.

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“…The boundary conditions considered here are either of the Neumann or Dirichlet type. Based on the complex-valued dual BEM , Chen et al, 1999a, 1999c, the dual boundary integral equations for smooth boundary points are …”

Section: Imaginary-part Dual Integral Formulation For a Two-dimenmentioning

confidence: 99%

A nonsingular integral formulation for the Helmholtz eigenproblems of a circular domain

Chen

Kuo

Chen

1999

Journal of the Chinese Institute of Engineers

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A nonsingular integral formulation for the Helmholtz eigenproblem is developed in this paper. This novel method contains only imaginary-part kernels instead of complex-part kernels in the complexvalued BEM. Based on the imaginary-part formulation without singular source, no singular or hypersingular integrals are present. Although this formulation avoids the computation of singular and hypersingular integrals, this approach results in spurious eigensolutions. After comparing the results from the dual formulation, the true and spurious solutions can be separated. An analytical example for the eigensolutions of a two-dimensional circular domain is studied. The continuous system can be transformed to a discrete system with circulants. Based on the spectral properties of circulants, the true and spurious solutions for the eigenvalues, boundary modes, interior modes and multiplicities are all examined. The possible failure of Hutchinson's sorting technique of looking at modal shapes is also discussed.

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Numerical experiments for acoustic modes of a square cavity using the dual boundary element method

Cited by 32 publications

References 23 publications

The Boundary Collocation Method With Meshless Concept for Acoustic Eigenanalysis of Two-Dimensional Cavities Using Radial Basis Function

The Boundary Collocation Method With Meshless Concept for Acoustic Eigenanalysis of Two-Dimensional Cavities Using Radial Basis Function

Applications of the Generalized Singular-Value Decomposition Method on the Eigenproblem Using the Incomplete Boundary Element Formulation

A nonsingular integral formulation for the Helmholtz eigenproblems of a circular domain

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