A new approach for the solution of the neighborhood problem in meshfree methods

Abstract

This article introduces a new point of view in the description and solution of neighborhood problems and, more specifically, to those arising in meshfree or simulations in computational mechanics. In particular, we focus on the solution of neighborhood computations when the problem involves two distinct sets of points whose positions change, and whose proximity needs to be repeatedly assessed. With this type of problems in mind, we reformulate the neighborhood concepts and propose a solution—implemented in an open source library—that possesses a simple interface, is suitable for parallelization, has very mild restrictions on the point data, depends only on the standard C++ library, and has a small memory impact. The presented algorithm employs hash tables to achieve constant time in point searches, integer lattices to define a grid of background cells, and classifies the two independent point sets. As a result, and in addition to the favorable features previously indicated, the method is very fast as compared with the available implementations for similar problem.