| 三维Helmholtz方程的边界点方法 |
| |
| 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. |
| |
| 作者姓名： | 祁慧芳 |
| |
| 作者单位： | 重庆师范大学数学学院 |
| |
| 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.
|
| 关 键 词： | 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 |
| 收稿时间： | 2017/1/23 0:00:00 |
On Boundary Node Method for 3-D Helmholtz Equation |
| |
| QI Hui-fang.On Boundary Node Method for 3-D Helmholtz Equation[J].Journal of Southwest China Normal University(Natural Science),2018,43(5):11-16. |
| |
| Authors: | QI Hui-fang |
| |
| Institution: | College of Mathematics, Chongqing Normal University, Chongqing 401331, China |
| |
| 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. |
| |
| Keywords: | meshless method Helmholtz equation boundary node method moving least-square indirect boundary integral equations |
| 本文献已被 CNKI 等数据库收录！ |
| 点击此处可从《西南师范大学学报(自然科学版)》浏览原始摘要信息 |
| 点击此处可从《西南师范大学学报(自然科学版)》下载免费的PDF全文 |
