Adaptivity for structured meshfree particle methods in 2D and 3D

The implementation of h-adaptivity for meshfree particle methods within a structured framework is described. In this framework, the initial particle arrangement is structured along with a background mesh, and outside boundaries and interior interfaces are described by implicit functions. The advantage of meshfree approximations in this framework lies in the ease of implementing h-adaptivity and the simplicity of the data structures. Particles can easily be added and removed without complications in the data structure, although there are some issues in the quadrature. An a posteriori error estimation is used for the adaptive refinement. An adaptive refinement strategy is applied to several linear elastic problems with high stress and strain gradients and singularities. Several non-linear examples are also given.