Year: 2014
Type: preprint
Abstract: We formulate and analyze an optimization-based Atomistic-to-Continuum (AtC) coupling method for problems with point defects. Near the defect core the method employs a potential-based atomistic model, which enables accurate simulation of the defect. Away from the core, where site energies become nearly independent of the lattice position, the method switches to a more efficient continuum model. The two models are merged by minimizing the mismatch of their states on an overlap region, subject to the atomistic and continuum force balance equations acting independently in their domains. We prove that the optimization problem is well-posed and establish error estimates.
Source: arXiv (Cornell University)
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, Skolkovo Institute of Science and Technology, Office of Science, National Nuclear Security Administration, National Defense Science and Engineering Graduate, Multidisciplinary University Research Initiative, Office of International Science and Engineering, Advanced Scientific Computing Research, Air Force Office of Scientific Research, Army Research Office, Sandia National Laboratories
Awards: G1281699269, G1523888516, G1626522811, G1867850364, G194215011, G2075401295, Collaborative Research: Novel Multiscale Computational Mathematics for Surface-Dominated Nanomaterials, G237582453, G3402382677, G3424441068, G3469581542, G351415096, G4805816520, G5735784432, G5964126404, G6071252945, G6485281451, THEORY AND COMPUTATION FOR MESOSCOPIC MATERIALS MODELING, PIRE: Science at the Triple Point Between Mathematics, Mechanics and Materials Science, G7318852158, G7452299184, G7830320759, G8456466421, G891797142
OpenAlex ID: W2949893677