基于当地笛卡尔架构的无网格方法

基金项目: 国家自然科学基金资助项目(10372055);上海市重点学科建设项目资助(Y0103)

Mesh Free Method Based on Local Cartesian Frame

Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, P. R. China

摘要: 提出了一种新的无网格方法，该方法是自动地在每一样点建立一个局部笛卡尔架构并选取相应的邻近点，然后运用全导数公式构造该样点的所有导数，它不需要任何网格单元，所以是彻底的无网格方法．数值算例表明，该方法具有很高的精度．
- 无网格 /
- 全导数 /
- 笛卡尔架构
Abstract: A new mesh free method proposed by the authors was presented in which the derivatives at each node were constructed using whole derivative formulas through the nodes selected around the node using local Cartesian frame in an autonomous manner,so that without any element it could be considered as a completely mesh free method.The method had been tested with a numerical example,and reliable solution was obtained with high accuracy and efficiency.
- mesh free /
- whole derivative /
- Cartesian frame

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