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2018 Volume 43 Issue 5
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QI Hui-fang. On Boundary Node Method for 3-D Helmholtz Equation[J]. Journal of Southwest China Normal University(Natural Science Edition), 2018, 43(5): 11-16. doi: 10.13718/j.cnki.xsxb.2018.05.003
Citation: QI Hui-fang. On Boundary Node Method for 3-D Helmholtz Equation[J]. Journal of Southwest China Normal University(Natural Science Edition), 2018, 43(5): 11-16. doi: 10.13718/j.cnki.xsxb.2018.05.003
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On Boundary Node Method for 3-D Helmholtz Equation

  • College of Mathematics, Chongqing Normal University, Chongqing 401331, China

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  • Received Date: 23/01/2017
  • Combining the moving least-square (MLS) method and boundary integral equations (BIEs), a meshless method, the boundary node method (BNM), is developed for the internal and external boundary value problems of the 3-D Helmholtz equation. The method converted Helmholtz equation into an indirect boundary integral equation using a single-layer potential theory, and the boundary integral equation is used to separate the indirect boundary integral equation. The integral with the basic solution will appear weakly singular when calculating, therefore, weak singularities need to be treated. Numerical examples showed the effectiveness of the boundary node method for solving indirect boundary integral equation.
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On Boundary Node Method for 3-D Helmholtz Equation

  • Received Date: 23/01/2017

Abstract: Combining the moving least-square (MLS) method and boundary integral equations (BIEs), a meshless method, the boundary node method (BNM), is developed for the internal and external boundary value problems of the 3-D Helmholtz equation. The method converted Helmholtz equation into an indirect boundary integral equation using a single-layer potential theory, and the boundary integral equation is used to separate the indirect boundary integral equation. The integral with the basic solution will appear weakly singular when calculating, therefore, weak singularities need to be treated. Numerical examples showed the effectiveness of the boundary node method for solving indirect boundary integral equation.

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