An interpolating boundary element-free method for three-dimensional potential problems
An interpolating boundary element-free method for three-dimensional potential problems
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三维潜在问题的无边界元插值方法
DOI：
10.1016/j.apm.2014.10.071
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发表时间：
2015-06
影响因子：
5
通讯作者：
Xiaolin Li
中科院分区：
文献类型：
--
作者：
Xiaolin Li
本文首先讨论了一种改进的插值移动最小二乘（IIMLS）方法及其形函数的性质。IIMLS方法的形函数具有δ函数性质，权函数具有非奇异性，克服了移动最小二乘法和插值移动最小二乘法的缺点。将边界积分方程与IIMLS方法相结合，发展了一种求解三维位势问题的插值边界无单元法。在IBEFM中，只需要域边界面上的节点数据结构。与边界节点法（BNM）不同，IBEFM是一种直接无网格法，其主要未知量是节点变量的真实的解，边界条件可以直接施加，计算精度高。此外，IBEFM中的未知量和系统方程的数量都只有BNM的一半，从而提高了计算速度和效率。曲线曲面拟合和潜在问题的数值算例表明，本文方法具有较高的效率和收敛速度。
This paper begins by discussing an improved interpolating moving least-square (IIMLS) method and the properties of its shape function. In the IIMLS method, the shape function is of delta function property and the weight function is nonsingular, so it overcomes the drawbacks in both the moving least-square approximation and the interpolating moving least-square method. Then combining boundary integral equations with the IIMLS method, an interpolating boundary element-free method (IBEFM) is developed for three-dimensional potential problems. In the IBEFM, only a nodal data structure on the boundary face of a domain is required. Unlike the boundary node method (BNM), the IBEFM is a direct meshless method in which the primary unknown quantities are real solutions of nodal variables, and boundary conditions can be imposed directly and easily, which leads to a greater computational precision. Besides, the number of both unknowns and system equations in the IBEFM is only half of that in the BNM, and thus the computing speed and efficiency are increased. Numerical examples on curve/surface fittings and potential problems indicate that the efficiency and convergence rate of the present methods is high.
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DOI：
10.1016/j.enganabound.2008.11.002
发表时间：
2009-06
影响因子：
3.3
作者：
Xiaolin Li;Jialin Zhu
通讯作者：
Xiaolin Li;Jialin Zhu
DOI：
10.1016/s0045-7825(96)01132-2
发表时间：
1997-04
影响因子：
7.2
作者：
Wing Kam Liu;Shaofan Li;T. Belytschko
通讯作者：
Wing Kam Liu;Shaofan Li;T. Belytschko
DOI：
10.1007/s11433-010-0159-1
发表时间：
2010-04
期刊：
Science China Physics, Mechanics and Astronomy
影响因子：
--
作者：
Hongping Ren;Yumin Cheng;Wu Zhang
通讯作者：
Hongping Ren;Yumin Cheng;Wu Zhang
DOI：
10.1002/(sici)1097-0207(19970830)40:16
发表时间：
1997-08
影响因子：
2.9
作者：
I. Kaljević;S. Saigal
通讯作者：
I. Kaljević;S. Saigal
DOI：
10.1016/j.enganabound.2007.10.010
发表时间：
2008-06
影响因子：
3.3
作者：
Hennadiy Netuzhylov
通讯作者：
Hennadiy Netuzhylov