Year: 2013
Type: preprint
Abstract: We present a new optimization-based method for atomistic-to-continuum (AtC) coupling. The main idea is to cast the coupling of the atomistic and continuum models as a constrained optimization problem with virtual Dirichlet controls on the interfaces between the atomistic and continuum subdomains. The optimization objective is to minimize the error between the atomistic and continuum solutions on the overlap between the two subdomains, while the atomistic and continuum force balance equations provide the constraints. Splitting of the atomistic and continuum problems instead of blending them and their subsequent use as constraints in the optimization problem distinguishes our approach from the existing AtC formulations. We present and analyze the method in the context of a one-dimensional chain of atoms modeled using a linearized two-body next-nearest neighbor interactions.
Source: arXiv (Cornell University)
Institutions: University of Minnesota, Sandia National Laboratories
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Funders: National Science Foundation, U.S. Department of Defense, U.S. Department of Energy, University of Minnesota, National Nuclear Security Administration, National Defense Science and Engineering Graduate, Office of International Science and Engineering, Advanced Scientific Computing Research, Air Force Office of Scientific Research, Sandia National Laboratories
Awards: G1523888516, G1626522811, G1867850364, G2075401295, G3402382677, G3469581542, "NEW; PREDICTIVE SIMULATION AND DESIGN OF MATERIALS BY QUASICONTINUUM AND ACCELERATED DYNAMICS METHODS; PI - MITCHELL LUSKIN", G4805816520, G5735784432, G6071252945, G6485281451, PIRE: Science at the Triple Point Between Mathematics, Mechanics and Materials Science, G7318852158, G7830320759, G8456466421, G891797142
OpenAlex ID: W2952900625