[BOOK][B] Multiple time scale dynamics

C Kuehn - 2015 - Springer
This book aims to provide an introduction to dynamical systems with multiple time scales. As
in any overview book, several topics are covered only quite briefly. My aim was to focus on …

Interfacing finite elements with deep neural operators for fast multiscale modeling of mechanics problems

M Yin, E Zhang, Y Yu, GE Karniadakis - Computer methods in applied …, 2022 - Elsevier
Multiscale modeling is an effective approach for investigating multiphysics systems with
largely disparate size features, where models with different resolutions or heterogeneous …

Atomistic-to-continuum coupling

M Luskin, C Ortner - Acta Numerica, 2013 - cambridge.org
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 …

Summation rules for a fully nonlocal energy-based quasicontinuum method

JS Amelang, GN Venturini, DM Kochmann - Journal of the Mechanics and …, 2015 - Elsevier
The quasicontinuum (QC) method coarse-grains crystalline atomic ensembles in order to
bridge the scales from individual atoms to the micro-and mesoscales. A crucial cornerstone …

Consistent energy-based atomistic/continuum coupling for two-body potentials in one and two dimensions

AV Shapeev - Multiscale Modeling & Simulation, 2011 - SIAM
This paper addresses the problem of consistent energy-based coupling of atomistic and
continuum models of materials, limited to zero-temperature statics of simple crystals. It has …

The quasicontinuum method: Theory and applications

DM Kochmann, JS Amelang - Multiscale materials modeling for …, 2016 - Springer
The quasicontinuum (QC) method has become a popular technique to bridge the gap
between atomistic and continuum length scales in crystalline solids. In contrast to many …

Atomistic/continuum blending with ghost force correction

C Ortner, L Zhang - SIAM Journal on Scientific Computing, 2016 - SIAM
We combine the ideas of atomistic/continuum energy blending and ghost force correction to
obtain an energy-based atomistic/continuum coupling scheme which has, for a range of …

Energy-based atomistic-to-continuum coupling without ghost forces

C Ortner, L Zhang - Computer Methods in Applied Mechanics and …, 2014 - Elsevier
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A refinement indicator for adaptive quasicontinuum approaches for structural lattices

L Chen, PZ Berke, TJ Massart, LAA Beex… - International Journal …, 2021 - Wiley Online Library
The quasicontinuum (QC) method is a concurrent multiscale approach in which lattice
models are fully resolved in small regions of interest and coarse‐grained elsewhere. Since …

Sharp stability estimates for the force-based quasicontinuum approximation of homogeneous tensile deformation

M Dobson, M Luskin, C Ortner - Multiscale Modeling & Simulation, 2010 - SIAM
The accuracy of atomistic-to-continuum hybrid methods can be guaranteed only for
deformations where the lattice configuration is stable for both the atomistic energy and the …