三维Helmholtz方程的边界点方法

祁慧芳

doi:10.13718/j.cnki.xsxb.2018.05.003

西南师范大学学报(自然科学版)

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三维Helmholtz方程的边界点方法

祁慧芳. 三维Helmholtz方程的边界点方法[J]. 西南师范大学学报(自然科学版), 2018, 43(5): 11-16. doi: 10.13718/j.cnki.xsxb.2018.05.003

引用本文:

祁慧芳. 三维Helmholtz方程的边界点方法[J]. 西南师范大学学报(自然科学版), 2018, 43(5): 11-16. doi: 10.13718/j.cnki.xsxb.2018.05.003

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

三维Helmholtz方程的边界点方法

祁慧芳

重庆师范大学数学学院, 重庆 401331

On Boundary Node Method for 3-D Helmholtz Equation

QI Hui-fang

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

摘要: 将移动最小二乘近似和边界积分方程相结合，提出了求解三维Helmholtz方程内外边值问题的无网格边界点方法.该方法用单层位势理论将Helmholtz方程转化为间接边界积分方程，并用边界点法离散间接边界积分方程.由于边界积分方程中含有基本解的积分计算时会出现弱奇异，详细推导了弱奇异积分的计算方式.数值算例表明了间接边界点法求解三维Helmholtz方程的有效性.
- 无网格方法 /
- Helmholtz方程 /
- 边界点方法 /
- 移动最小二乘近似 /
- 间接边界积分方程
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.
- meshless method /
- Helmholtz equation /
- boundary node method /
- moving least-square /
- indirect boundary integral equations .

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三维Helmholtz方程的边界点方法

祁慧芳

重庆师范大学数学学院, 重庆 401331

收稿日期: 2017-01-23

关键词:

摘要: 将移动最小二乘近似和边界积分方程相结合，提出了求解三维Helmholtz方程内外边值问题的无网格边界点方法.该方法用单层位势理论将Helmholtz方程转化为间接边界积分方程，并用边界点法离散间接边界积分方程.由于边界积分方程中含有基本解的积分计算时会出现弱奇异，详细推导了弱奇异积分的计算方式.数值算例表明了间接边界点法求解三维Helmholtz方程的有效性.

English Abstract

On Boundary Node Method for 3-D Helmholtz Equation

重庆师范大学数学学院, 重庆 401331

Received Date: 2017-01-23

Keywords:

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.