Improved non-singular local boundary integral equation method

作     者：付东杰 陈海波 张培强 

作者机构：Department of Modern Mechanics University of Science and Technology of China Hefei 230026P.R.China CAS Key Laboratory of Mechanical Behavior and Design of MaterialsUniversity of Science and Technology of ChinaHefei 230026P.R.China 

出 版 物：《Applied Mathematics and Mechanics(English Edition)》 (应用数学和力学（英文版）)

年 卷 期：2007年第28卷第8期

页      面：1093-1099页

核心收录：

学科分类：07[理学] 08[工学] 070104[理学-应用数学] 0701[理学-数学] 0801[工学-力学（可授工学、理学学位）] 

主　　题：meshless method local boundary integral equation method moving least square approximation singular integrals 

摘      要：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 al- gorithm. 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.