On boundary conditions in the element-free Galerkin method
On boundary conditions in the element-free Galerkin method
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DOI：
10.1007/s004660050175
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发表时间：
1997-03
影响因子：
4.1
通讯作者：
Y. Mukherjee;S. Mukherjee
中科院分区：
文献类型：
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作者：
Y. Mukherjee;S. Mukherjee
在无单元伽辽金 (EFG) 方法中准确施加基本边界条件通常会遇到困难，因为该方法中使用的移动最小二乘法 (MLS) 插值缺乏常用有限元或边界元方法形状函数的 delta 函数属性。本文提出了一种简单且合乎逻辑的策略来缓解上述问题。在 EFG 方法中，离散范数通常被最小化，以获得某些可变系数。这项工作提出的策略涉及到这种离散规范的新定义。对于此处介绍的二维潜在问题，这种新策略在所有数值示例中都非常有效。除了边界条件的讨论之外，本文还提出了一些关于细化策略的建议，以提高 EFG 方法数值解的精度。
Accurate imposition of essential boundary conditions in the Element Free Galerkin (EFG) method often presents difficulties because the Moving Least Squares (MLS) interpolants, used in this method, lack the delta function property of the usual finite element or boundary element method shape functions. A simple and logical strategy, for alleviating the above problem, is proposed in this paper. A discrete norm is typically minimized in the EFG method in order to obtain certain variable coefficients. The strategy proposed in this work involves a new definition of this discrete norm. This new strategy works very well in all the numerical examples, for 2-D potential problems, that are presented here. In addition to the discussion of boundary conditions, some recommendations are also made in this paper regarding strategies for refinements in order to improve the accuracy of numerical solutions from the EFG method.