A meshless quasicontinuum method based on local maximum-entropy interpolation
Coarse-graining atomistic ensembles can overcome the practical limitations of molecular statics and dynamics in order to facilitate simulations at much larger length scales than accessible by discrete atomistic techniques due to computational expense. The quasicontinuum (QC) method was introduced to reduce the number of degrees of freedom in crystalline solids by choosing a set of representative atoms from the fully atomistic ensemble and obtaining the positions and momenta of all remaining lattice sites by interpolation. Here, we present a new energy-based nonlocal meshless version of the QC method based on local maximum-entropy (max-ent) interpolation schemes instead of the traditional polynomial interpolation, which particularly promises advantages in model adaptation to tie atomistic resolution to crystal defects while efficiently coarse-graining away from these. To this end, we formulate the meshless QC representation and analyze its performance. One-dimensional chain problems allow for clean mathematical treatment and provide interesting insight, which allow us to quantify the approximation error as a function of representative atom distribution and support of meshless shape functions. A fully three-dimensional implementation then demonstrates the applicability of the new QC scheme and highlights its features. Overall, we show that local max-ent interpolation offers a number of advantages over previous QC realizations.