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Stable time step estimates for mesh‐free particle methods
Author(s) -
Joldes Grand Roman,
Wittek Adam,
Miller Karol
Publication year - 2012
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.4290
Subject(s) - computer science , point (geometry) , algorithm , finite element method , time domain , stability (learning theory) , material point method , mathematical optimization , numerical integration , domain (mathematical analysis) , mathematics , engineering , geometry , mathematical analysis , structural engineering , machine learning , computer vision
SUMMARY Real‐time computational biomechanics for medicine usually uses explicit time integration, because of its efficiency and suitability for parallel implementation. Explicit time integration is only conditionally stable and therefore requires an estimation of the maximum stable time step that can be used. In this paper we develop a method of estimating the stable time step for mesh‐free particle methods for a specific case of mass lumping: the mass associated with an integration point is distributed equally to all nodes found in the support domain of that integration point. Two estimates of the stable time step for each integration point are developed: one that is very accurate but more costly to compute and one less accurate but easier to implement. The results are also valid for the FEM and beyond computational biomechanics for medicine. Copyright © 2012 John Wiley & Sons, Ltd.