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    Using the Method of Fundamental Solutions for Obtaining Exponentially Convergent Helmholtz Eigensolutions

    Chia-Cheng Tsai1,2, D. L. Young3

    CMES-Computer Modeling in Engineering & Sciences, Vol.94, No.2, pp. 175-205, 2013, DOI:10.3970/cmes.2013.094.175

    Abstract It is well known that the method of fundamental solutions (MFS) is a numerical method of exponential convergence. In this study, the exponential convergence of the MFS is demonstrated by obtaining the eigensolutions of the Helmholtz equation. In the solution procedure, the sought solution is approximated by a superposition of the Helmholtz fundamental solutions and a system matrix is resulted after imposing the boundary condition. A golden section determinant search method is applied to the matrix for finding exponentially convergent eigenfrequencies. In addition, the least-squares method of fundamental solutions is applied for solving the corresponding More >

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