Blended Atomistic-to-Continuum coupling analyses and methods

This article considers the blending of atomistic and continuum problems on a bridging subdomain building upon the ideas introduced in [1, 2, 7]. The continuity of the atomistic and continuum solutions is imposed by a constraint operator using Lagrange multipliers. These methods are stated in an abstract form. The consistency of these methods is analyzed. A new blending model is designed using mechanical arguments. The consistency and accuracy of the method is discussed theoretically and confirmed numerically. ∗Computational Mathematics and Algorithms, MS-1320, Sandia National Laboratories, Albuquerque, NM 87185-1320, ({sibadia,pbboche,rblehou,mlparks}@sandia.gov). †School of Computational Science, Florida State University, Tallahassee, FL 32306-4120, ([email protected])