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Abstract

This study adopts a meshless numerical method, the combination of the method of fundamental solutions (MFS) and method of particular solutions (MPS) following the lead of Reutskiy, to determine the eigenfrequencies of four different waveguides, based on the principle of physical response of a system exposed to external source. The response amplitudes to determine the resonant frequencies for the eigenproblems are used. We use the MFS with external source (MFS-ES) and MPS to solve a sequence of inhomogeneous problems for the determination of the eigenfrequencies. This is an alternative to the typical methods of directly solving the homogeneous matrix system to search for the eigenvalues in an eigenproblem. The square, elliptic, concentric annular and eccentric annular waveguides are analyzed to demonstrate the capability and robustness of the present meshless numerical method. In the numerical experiments, the computational results are not sensitive at all to the locations of the external source. Furthermore, the spurious eigenfrequencies will not occur in this boundary-type meshless method which is different from other numerical methods.

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