Atomistic to Continuum Coupling

Crystal defects demand atomistic modeling near defect cores for accuracy and continuum modeling to capture long-range elastic interactions for efficiency.  To address this modeling problem, material scientists have proposed a plethora of hybrid atomistic-to-continuum coupling methods. Luskin and his collaborator Ortner have formulated a novel and general numerical analysis of these methods and derived quasi-optimal methods that balance the errors of coupling, continuum approximation, and far field boundary conditions.

M. Luskin, C. Ortner, and B. Van Koten. Formulation and optimization of the energy-based blended quasicontinuum method. Comput. Methods Appl. Mech. Engrg., 253:160–168, 2013.

M. Luskin and C. Ortner. Atomistic-to-continuum coupling. Acta Numer., 22:397–508, 2013.

X. H. Li, M. Luskin, C. Ortner, and A. V. Shapeev. Theory-based benchmarking of the blended force-based quasicontinuum method. Comput. Methods Appl. Mech. Engrg., 268:763–781, 2014.