An Analysis of Node-Based Cluster Summation Rules in the Quasicontinuum Method

Details An Analysis of Node-Based Cluster Summation Rules in the Quasicontinuum Method An Analysis of Node-Based Cluster Summation Rules in the Quasicontinuum Method

2008-11-26

arxiv.org/abs/0811.4214v1

SIAM. J. Numer. Anal., 47:3070-3086, 2009

Mathematics

Numerical Analysis

20 pages, 2 figures

Scientific paper

We investigate two examples of node-based cluster summation rules that have been proposed for the quasicontinuum method: a force-based approach (Knap & Ortiz, J. Mech. Phys. Solids 49, 2001), and an energy-based approach which is a generalization of the non-local quasicontinuum method (Eidel & Stukowski, J. Mech. Phys. Solids, to appear). We show that, even for the case of nearest neighbour interaction in a one-dimensional periodic chain, both of these approaches create large errors when used with graded and, more generally, non-smooth meshes. These errors cannot be removed by increasing the cluster size. We offer some suggestions how the accuracy of (cluster) summation rules may be improved.

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