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Adaptivity for structured meshfree particle methods in 2D and 3D
Author(s) -
Rabczuk T.,
Belytschko T.
Publication year - 2005
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1326
Subject(s) - meshfree methods , quadrature (astronomy) , adaptive mesh refinement , computer science , a priori and a posteriori , smoothed particle hydrodynamics , gravitational singularity , finite element method , mathematics , mathematical optimization , algorithm , computational science , mathematical analysis , structural engineering , mechanics , philosophy , electrical engineering , epistemology , physics , engineering
Abstract 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. Copyright © 2005 John Wiley & Sons, Ltd.