Improved non-singular local boundary integral equation method
- 36 Downloads
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 wordsmeshless method local boundary integral equation method moving least square approximation singular integrals
Chinese Library ClassificationO302
2000 Mathematics Subject Classification70E05
Unable to display preview. Download preview PDF.
- Zhang Xiong, Liu Yan. Meshless methods[M]. Beijing: Tsinghua University Publishing Company, 2004 (in Chinese).Google Scholar
- Guo Xiaofeng, Chen Haibo, Wang Ningyu, et al. Meshless regularized local boundary integral equation method to 2D potential problems[J]. Journal of University of Science and Technology of China, 2006, 36(6):636–640 (in Chinese).Google Scholar
- Chen H B, Fu D J, Zhang P Q. An investigation of Helmholtz problems with high wave numbers via the meshless LBIEM[M]. In: Sivakumar S M, Prasad A Meher, Dattaguru B, et al. (eds). Advances in Computational & Experimental Engineering and Sciences (Proceeding of ICCES’05, 1–10 December 2005, India), Tech Science Press, 2005, 114–119.Google Scholar
- Chen H B, Fu D J, Zhang P Q. An investigation of wave propagation with high wave numbers via the regularized LBIEM[J]. CMES-Computer Modeling in Engineering Sciences, 2008, 583(1):1–14.Google Scholar