Force-based atomistic/continuum blending for multilattices
D. Olson, X. Li, B. C. Ortner and Van Koten,
Numerische Mathematik, 140, 703–754 (2018).


We formulate the blended force-based quasicontinuum method for multilattices and develop rigorous error estimates in terms of the approximation parameters: choice of atomistic region, blending region, and continuum finite element mesh. Balancing the approximation parameters yields a convergent atomistic/continuum multiscale method for multilattices with point defects, including a rigorous convergence rate in terms of the computational cost. The analysis is illustrated with numerical results for a Stone-Wales defect in graphene.