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Some problems with the method of fundamental solution using radial basis functions

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Abstract

The present work describes the application of the method of fundamental solutions (MFS) along with the analog equation method (AEM) and radial basis function (RBF) approximation for solving the 2D isotropic and anisotropic Helmholtz problems with different wave numbers. The AEM is used to convert the original governing equation into the classical Poisson’s equation, and the MFS and RBF approximations are used to derive the homogeneous and particular solutions, respectively. Finally, the satisfaction of the solution consisting of the homogeneous and particular parts to the related governing equation and boundary conditions can produce a system of linear equations, which can be solved with the singular value decomposition (SVD) technique. In the computation, such crucial factors related to the MFS-RBF as the location of the virtual boundary, the differential and integrating strategies, and the variation of shape parameters in multi-quadric (MQ) are fully analyzed to provide useful reference.

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Authors and Affiliations

  1. College of Civil Engineering and Architecture, Henan University of Technology, Zhengzhou, 450052, China

    Hui Wang

  2. Department of Mechanics, Tianjin University, Tianjin, 300072, China

    Hui Wang

  3. Department of Engineering, Australian National University, Canberra, ACT, 0200, Australia

    Qinghua Qin

Authors
  1. Hui Wang
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  2. Qinghua Qin
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Wang, H., Qin, Q. Some problems with the method of fundamental solution using radial basis functions. Acta Mech. Solida Sin. 20, 21–29 (2007). https://doi.org/10.1007/s10338-007-0703-3

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  • DOI: https://doi.org/10.1007/s10338-007-0703-3

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