We formulate and analyze an optimization-based Atomistic-to-Continuum (AtC) coupling method for problems with point defects. Application of a potential-based atomistic model near the defect core 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.
|Number of pages||41|
|Journal||ESAIM: Mathematical Modelling and Numerical Analysis|
|Publication status||Published - 1 Jan 2016|
- Atomic lattice
- Atomistic-to-continuum coupling
- Constrained optimization
- Point defect