2014/11/14 by Derek Olson, Olson, Derek, Alexander V. Shapeev +5
Materials Science · Physics and Astronomy · #FOS: Mathematics #Fusion materials and technologies #Microstructure and mechanical properties #Numerical Analysis (math.NA) #Surface and Thin Film Phenomena
paper · pdf · doi:10.48550/arxiv.1411.4027
openalex publication_date 2014/11/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
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.