| SOME PROBLEMS WITH THE METHOD OF FUNDAMENTAL SOLUTION USING RADIAL BASIS FUNCTIONS |
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| 作者姓名： | References： |
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| 作者单位： | Wang Hui (College of Civil Engineering and Architecture，Henan University of Technology，Zhengzhou 450052，China) (Department of Mechanics，Tianjin University，Tianjin 300072，China) Qin Qinghua (Department of Engineering，Australian National University，Canberra，ACT 0200，Australia) |
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| 摘 要： | 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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| 关 键 词： | 径向基函数 基本解 奇异值分解 无网格法 |
| 收稿时间： | 2006-03-23 |
| 修稿时间： | 2006-11-28 |
SOME PROBLEMS WITH THE METHOD OF FUNDAMENTAL SOLUTION USING RADIAL BASIS FUNCTIONS |
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| Wang Hui,Qin Qinghua.SOME PROBLEMS WITH THE METHOD OF FUNDAMENTAL SOLUTION USING RADIAL BASIS FUNCTIONS[J].Acta Mechanica Solida Sinica,2007,20(1):21-29. |
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| Authors: | Wang Hui Qin Qinghua |
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| Affiliation: | 1. College of Civil Engineering and Architecture, Henan University of Technology, Zhengzhou 450052, China;2. Department of Mechanics, Tianjin University, Tianjin 300072, China;3. Department of Engineering, Australian National University, Canberra, ACT 0200, Australia;1. Aerospace Engineering Department, Faculty of New Sciences & Technologies, University of Tehran, Tehran, Iran;2. Department of Mechanical Engineering, College of Engineering, Qom University of Technology, Qom, Iran;1. University of Ljubljana, Faculty of Natural Sciences and Engineering, Aškerčeva cesta 12, Ljubljana, Slovenia;2. Department of Mathematics, Hong Kong Baptist University, Hong Kong;3. University of Ljubljana, Faculty of Civil and Geodetic Engineering, Jamova cesta 2, Ljubljana, Slovenia |
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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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| Keywords: | meshless method analog equation method method of fundamental solution radial basis function singular value decomposition Helmholtz equation |
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