A review of local-to-nonlocal coupling methods in nonlocal diffusion and nonlocal mechanics

M D'Elia, X Li, P Seleson, X Tian, Y Yu - Journal of Peridynamics and …, 2021 - Springer
Abstract Local-to-nonlocal (LtN) coupling refers to a class of methods aimed at combining
nonlocal and local modeling descriptions of a given system into a unified coupled …

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 …

Analysis of boundary conditions for crystal defect atomistic simulations

V Ehrlacher, C Ortner, AV Shapeev - Archive for Rational Mechanics and …, 2016 - Springer
Numerical simulations of crystal defects are necessarily restricted to finite computational
domains, supplying artificial boundary conditions that emulate the effect of embedding the …

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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Geometry equilibration of crystalline defects in quantum and atomistic descriptions

H Chen, FQ Nazar, C Ortner - Mathematical Models and Methods in …, 2019 - World Scientific
We develop a rigorous framework for modeling the geometry equilibration of crystalline
defects. We formulate the equilibration of crystal defects as a variational problem on a …

Analysis of blended atomistic/continuum hybrid methods

XH Li, C Ortner, AV Shapeev, B Van Koten - Numerische Mathematik, 2016 - Springer
We present a comprehensive error analysis of two prototypical atomistic-to-continuum
coupling methods of blending type: the energy-based and the force-based quasicontinuum …

Generalized bridging domain method for coupling finite elements with discrete elements

F Tu, D Ling, L Bu, Q Yang - Computer Methods in Applied Mechanics and …, 2014 - Elsevier
The concurrent coupling of finite elements and discrete elements is an effective DOF
reduction methodology for reproducing the granular flow phenomenon as discrete element …

Adaptive Multiscale Coupling Methods of Molecular Mechanics based on a Unified Framework of a Posteriori Error Estimates

H Wang, Y Wang - arxiv preprint arxiv:2309.13255, 2023 - arxiv.org
Multiscale coupling methods are significant methodologies for the modeling and simulation
of materials with defects, intending to achieve the (quasi-) optimal balance of accuracy and …