二维各向异性位势问题的改进插值型边界无单元法  

An Improved Interpolating Boundary Element-Free Method with Nonsingular Weight Function for Two-Dimensional Anisotropic Potential Problems

作　　者：秦丽 李小林 QIN Li;LI Xiaolin(College of Mathematics Science,Chongqing Normal University,Chongqing 401331,China)

机构地区：[1]重庆师范大学数学科学学院,重庆401331

出　　处：《重庆师范大学学报（自然科学版）》2019年第2期66-72,共7页Journal of Chongqing Normal University:Natural Science

摘　　要：【目的】把边界积分方程方法和基于非奇异权函数的改进移动最小二乘插值法相结合,建立数值求解二维各向异性位势问题的改进插值型边界无单元法。【方法】在改进移动最小二乘插值法的基础上,讨论了非奇异权函数的改进移动最小二乘插值法,它的形函数满足Kroneckerδ函数的性质,因此可以直接施加边界条件。【结果】数值算例表明该方法求解二维各向异性位势问题是有效和可行的。【结论】与边界元方法相比,该方法精度和收敛性更好。[Purposes]Combining the boundary integral equation method with the improved interpolating moving least-square method(IIMLS)based on nonsingular weight functioan improved interpolating boundary element-free method(IIBEFM)is developed for solving two-dimensional anisotropic potential problems.[Methods]On the basis of the improved moving least-square interpolation method.the improved interpolating moving least-square interpolation method with nonsingular weight function is discussed.Its shape function satisfies the property of Kronecker delta function丒 so boundary conditions can be applied directly.[Findings]Numerical examples show that the method is effective and feasible for solving two-dimensional an isotropic potential problems.[Conclusions]Compared with the boundary element method,this method has better accuracy and convergence.

关 键 词：各向异性 位势问题 非奇异权函数的改进移动最小二乘插值法 改进插值型边界无单元法 

分 类 号：O241.82[理学—计算数学]