On h-Adaptivity Analysis Using Multiple Scale Reproducing Kernel Particle Method and Partition of Unity Quadrature

摘要

The present work describes a framework of h-adaptivity analysis implemented by multiple scale reproducing kernel particle method (RKPM) and the numerical integration technique based on the theory of partition of unity (PU). The multiple scale RKPM is briefly reviewed, and the penalty method for imposing the essential boundary conditions is employed subsequently. In order to solve the derived integrals, the general formulas of PU quadrature are derived, and the approach to generate the patches and to calculate the PU functions is proposed in details. Furthermore, with the edge detection technique (extreme detection with a threshold) and the node refinement strategy (local Delaunay triangulation), the whole scheme of h-adaptivity analysis is given. The feasibility, convergence and performance of the proposed h-adaptivity analysis scheme are demonstrated by the results of two numerical examples.