A point interpolation meshless method based on radial basis functions
A point interpolation meshless method based on radial basis functions
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DOI：
10.1002/nme.489
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发表时间：
2002-08
影响因子：
2.9
通讯作者：
Jian-Guo Wang;Guirong Liu
中科院分区：
文献类型：
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作者：
Jian-Guo Wang;Guirong Liu
提出了一种基于径向基函数和多项式基函数相结合的点插值无网格法。径向基函数的引入克服了仅基于多项式基的无网格法可能存在的奇异性。这种非奇异性在构造性能良好的形函数时很有用。此外，所得到的插值函数遍历影响域中的所有散乱点，因此形函数具有Delta函数性质。这使得本质边界条件的实现比基于移动最小二乘近似的无网格方法容易得多。此外，形函数的偏导数易于获得，从而提高了计算效率。曲线曲面拟合和固体力学问题的算例表明，该方法具有较高的精度和收敛速度。版权所有©2002 John Wiley&Sons，Ltd.
A point interpolation meshless method is proposed based on combining radial and polynomial basis functions. Involvement of radial basis functions overcomes possible singularity associated with the meshless methods based on only the polynomial basis. This non‐singularity is useful in constructing well‐performed shape functions. Furthermore, the interpolation function obtained passes through all scattered points in an influence domain and thus shape functions are of delta function property. This makes the implementation of essential boundary conditions much easier than the meshless methods based on the moving least‐squares approximation. In addition, the partial derivatives of shape functions are easily obtained, thus improving computational efficiency. Examples on curve/surface fittings and solid mechanics problems show that the accuracy and convergence rate of the present method is high. Copyright © 2002 John Wiley & Sons, Ltd.