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A subdomain collocation method based on Voronoi domain partition and reproducing kernel approximation

机译:基于Voronoi域分区和再现核逼近的子域配置方法

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A subdomain collocation reproducing kernel approximation method is proposed. Subdomains are constructed by nonoverlapping Voronoi cells and a local weak form is defined over these subdomains. The standard RKPM shape functions are used directly for approximation, while weighting functions of the subdomain collocation method hold a constant value of unit only over a specific Voronoi cell. The body integration of the local weak form is now converted into much cheaper and efficient contour integration along the boundaries of Voronoi cells. It does not need to impose traction free boundary conditions explicitly in contrast to point collocation method. Furthermore, the method provides a natural background structure for performing h-adaptivity analysis straightforwardly. All these features constitute the subdomain collocation method a promising alternative to standard Galerkin method and point collocation method. Some elastostatics examples are presented to demonstrate the effectiveness, the convergence property, and the adaptivity performance of present method.
机译:提出了一种子域搭配的再生核逼近方法。子域是通过不重叠的Voronoi细胞构建的,并且在这些子域上定义了局部弱形式。标准RKPM形状函数直接用于近似,而子域搭配方法的加权函数仅在特定Voronoi单元上保持单位常数。现在,沿着Voronoi细胞的边界将局部弱形式的身体整合转换为便宜得多且有效的轮廓整合。与点配置方法相反,它不需要明确地施加无牵引力边界条件。此外,该方法提供了用于直接进行h适应性分析的自然背景结构。所有这些特征构成了子域配置方法,可以替代标准的Galerkin方法和点配置方法。给出了一些静电静力例子来证明本方法的有效性,收敛性和适应性。

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