A partitioned-domain multiscale method is a computational framework in which certain key
regions are modeled atomistically while most of the domain is treated with an approximate …

This work gives an overview of the theoretical background and of the numerical modelling
framework used to describe the mechanical properties and the response of materials on …

The aim of this monograph is to describe the main concepts and recent-vances in
multiscale? nite element methods. This monograph is intended for …

Atomistic-to-continuum (a/c) coupling methods are a class of computational multiscale
schemes that combine the accuracy of atomistic models with the efficiency of continuum …

This book develops a systematic and rigorous mathematical theory of finite difference
methods for linear elliptic, parabolic and hyperbolic partial differential equations with …

For a next-nearest neighbour pair interaction model in a periodic domain, a priori and a
posteriori analyses of the quasinonlocal quasicontinuum method (QNL-QC) are presented …

The accuracy of the quasi-continuum method is analyzed using a series of models with
increasing complexity. It is demonstrated that the existence of the ghost force may lead to …

Due to their algorithmic simplicity and high accuracy, force-based model coupling
techniques are popular tools in computational physics. For example, the force-based …

Multiscale modeling aims to solve problems at the engineering (macro) scale while
considering the complexity of the microstructure with minimum cost. Generally, two scales …

The atomistic to continuum interface for quasicontinuum energies exhibits nonzero forces
under uniform strain that have been called ghost forces. In this paper, we prove for a …