Adaptive Cloud Refinement (ACR) - Adaptation in Meshless Framework

Abstract

In the present work adaptation in meshless framework is proposed. The grid adaptation or mesh adaptation is quite well developed area in case of conventional grid based solvers and is popularly known as Adaptive mesh refinement (AMR). In such cases the adaptation is done by subdividing the cells or elements into finer cells or elements. In case of meshless methods there are no cells or elements but only a cloud of points. In this work we propose to achieve the meshless adaptation by locally refining the point density in the regions demanding higher resolution. This results into an adaptive enriched cloud of points. We call this method as Adaptive Cloud Refinement (ACR). The meshless solvers need connectivity information, which is a set of neighboring nodes. It is crucial part of meshless solvers. Obviously because of refining point density, the connectivity of nodes in such regions gets modified and hence has to be updated. An efficient connectivity update must exploit the fact that the node distribution would be largely unaffected except the region of adaptation. Hence connectivity updating needs to be done locally, only in these regions. In this paper we also present an extremely fast algorithm to update connectivity over adapted cloud called as ACU (Automatic Connectivity Update).