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

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.