Applied Mathematics and Mechanics (English Edition) ›› 2007, Vol. 28 ›› Issue (8): 1093-1099 .doi: https://doi.org/10.1007/s10483-007-0811-z
• 论文 • 上一篇 下一篇
付东杰, 陈海波, 张培强
收稿日期:
修回日期:
出版日期:
发布日期:
通讯作者:
FU Dong-jie, CHEN Hai-bo, ZHANG Pei-qiang
Received:
Revised:
Online:
Published:
Contact:
Abstract: When the source nodes are on the global boundary in the implementation of local boundary integral equation method (LBIEM), singularities in the local boundary integrals need to be treated specially. In the current paper, local integral equations are adopted for the nodes inside the domain and moving least square approximation (MLSA) for the nodes on the global boundary, thus singularities will not occur in the new algorithm. At the same time, approximation errors of boundary integrals are reduced significantly. As applications and numerical tests, Laplace equation and Helmholtz equation problems are considered and excellent numerical results are obtained. Furthermore, when solving the Helmholtz problems, the modified basis functions with wave solutions are adapted to replace the usually-used monomial basis functions. Numerical results show that this treatment is simple and effective and its application is promising in solutions for the wave propagation problem with high wave number.
Key words: moving least square approximation, meshless method, local boundary integral equation method, singular integrals
中图分类号:
O302
70E05
付东杰;陈海波;张培强. Improved non-singular local boundary integral equation method[J]. Applied Mathematics and Mechanics (English Edition), 2007, 28(8): 1093-1099 .
FU Dong-jie;CHEN Hai-bo;ZHANG Pei-qiang. Improved non-singular local boundary integral equation method[J]. Applied Mathematics and Mechanics (English Edition), 2007, 28(8): 1093-1099 .
0 / / 推荐
导出引用管理器 EndNote|Reference Manager|ProCite|BibTeX|RefWorks
链接本文: https://www.amm.shu.edu.cn/CN/10.1007/s10483-007-0811-z
https://www.amm.shu.edu.cn/CN/Y2007/V28/I8/1093