An improved meshless Shepard and least squares method possessing the delta property and requiring no singular weight function
An improved meshless Shepard and least squares method possessing the delta property and requiring no singular weight function
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一种改进的无网格Shepard和最小二乘法，具有δ性质且无需奇异权函数
DOI：
10.1007/s00466-013-0912-1
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发表时间：
2014-02
影响因子：
4.1
通讯作者：
Augarde, Charles
中科院分区：
文献类型：
--
作者：
Zhuang, Xiaoying;Zhu, Hehua;Augarde, Charles
无网格谢泼德和最小二乘（MSLS）方法和无网格谢泼德方法是基于单位分解的无网格插值方法，它克服了其它无网格方法难以直接施加本质边界条件等问题。但是，这两种方法都必须使用奇异权函数来增强逼近插值性，从而导致逼近结果的光滑性和局部振荡。本文利用双重定义的节点支撑，提出了一种改进的MSLS插值方法，使得不需要奇异权函数。所提出的插值方法满足边界节点的delta性质和整个区域的相容性条件，并且能够精确地再现基函数。该插值方法的计算量远低于移动最小二乘逼近法，而移动最小二乘逼近法可能是目前应用最广泛的无网格插值方法。
The meshless Shepard and least squares (MSLS) method and the meshless Shepard method are partition of unity based meshless interpolations which eliminate the problems by other meshless methods such as the difficulty in direct imposition of the essential boundary conditions. However, singular weight functions have to be used in both methods to enforce the approximation interpolatory, which leads to the loss of smoothness in approximation and locally oscillatory results. In this paper, an improved MSLS interpolation is developed by using dually defined nodal supports such that no singular weight function is required. The proposed interpolation satisfies the delta property at boundary nodes and the compatibility condition throughout the domain, and is capable of exactly reproducing the basis function. The computational cost of the present interpolation is much lower than the moving least-squares approximation which is probably the most widely used meshless interpolation at present.
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