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| Method of fundamental solution and boundary knot method for helmholtz equations: a comparative study |
| Received:November 13, 2009 Revised:September 02, 2010 |
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| DOI：10.7511/jslx201103006 |
| KeyWord:method of fundamental solution boundary knot method radial basis function Helmholtz equation |
| Author | Institution |
| 姜欣荣 |
河海大学 工程力学系,工程与科学数值模拟软件中心,南京 |
| 陈文 |
河海大学 工程力学系,工程与科学数值模拟软件中心,南京 |
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| Abstract: |
| Both the method of fundamental solution (MFS) and the boundary knot method (BKM) are RBF-based boundary-type meshless methods. This paper makes a comparative study of these two numerical methods in solving the Helmholtz equation under various regions, in terms of accuracy, symmetry, ill-conditioned interpolation matrix, and computational cost. Numerical results show that both methods can effectively solve the Helmholtz problems. In the discretization process, both methods can reduce the condition numbers by adjusting the location of the source points and collocation points. It is noted that the BKM interpolation matrix is symmetric while the MFS one is not. In addition, the BKM demands less CPU time than the MFS and requires a half memory of the MFS. |
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