Convergence of a Force-Based Hybrid Method in Three Dimensions
Article first published online: 23 OCT 2012
Copyright © 2012 Wiley Periodicals, Inc.
Communications on Pure and Applied Mathematics
Volume 66, Issue 1, pages 83–108, January 2013
How to Cite
Lu, J. and Ming, P. (2013), Convergence of a Force-Based Hybrid Method in Three Dimensions. Comm. Pure Appl. Math., 66: 83–108. doi: 10.1002/cpa.21429
- Issue published online: 23 OCT 2012
- Article first published online: 23 OCT 2012
- Manuscript Revised: DEC 2011
- Manuscript Received: FEB 2011
We study a force-based hybrid method that couples an atomistic model with the Cauchy-Born elasticity model. We show that the proposed scheme converges to the solution of the atomistic model with second-order accuracy, since the ratio between lattice parameter and the characteristic length scale of the deformation tends to 0. Convergence is established for the three-dimensional system without defects, with general finite-range atomistic potential and simple lattice structure. The proof is based on consistency and stability analysis. General tools for stability analysis are developed in the framework opseudodifference operators in arbitrary dimensions. © 2012 Wiley Periodicals, Inc.