We investigate two examples of node-based cluster summation rules that have been proposed for the quasicontinuum (QC) method: a force-based approach and an energy-based approach which is a generalization of the nonlocal QC method. We show that, even for the case of nearest-neighbor interaction in a one-dimensional periodic chain, both of these approaches create large errors that cannot be removed by increasing the cluster size when used with graded and, more generally, nonsmooth meshes. We offer some suggestions for how the accuracy of (cluster) summation rules may be improved.
|Original language||English (US)|
|Number of pages||17|
|Journal||SIAM Journal on Numerical Analysis|
|State||Published - 2009|
Bibliographical noteFunding Information:
This author's research was supported by EPSRC Critical Mass Project "New Frontiers in the Mathematics of Solids."
© 2009 Society for Industrial and Applied Mathematics.
- Atomistic-to-continuum coupling
- Cluster summation rule
- Quasicontinuum method