Regularized Meshless Method for Solving Acoustic Eigenproblem with Multiply-Connected Domain
K.H. Chen; J.T. Chen; and J.H. Kao

doi:10.3970/cmes.2006.016.027
Source CMES: Computer Modeling in Engineering & Sciences, Vol. 16, No. 1, pp. 27-40, 2006
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Keywords Regularized meshless method, Hypersingularity, Eigenvalue, Eigenmode, Method of fundamental solutions, Acoustics.
Abstract In this paper, we employ the regularized meshless method (RMM) to search for eigenfrequency of two-dimension acoustics with multiply-connected domain. The solution is represented by using the double layer potentials. The source points can be located on the physical boundary not alike method of fundamental solutions (MFS) after using the proposed technique to regularize the singularity and hypersingularity of the kernel functions. The troublesome singularity in the MFS methods is desingularized and the diagonal terms of influence matrices are determined by employing the subtracting and adding-back technique. Spurious eigenvalues are filtered out by using singular value decomposition (SVD) updating term technique. The accuracy and stability of the RMM are verified through the numerical experiments of the Dirichlet and Neumann problems for domains with multiple holes. The method is found to perform pretty well in comparison with analytical solutions and numerical results of boundary element method, finite element method and the point-matching method.
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