Analysis of a prototypical multiscale method coupling atomistic and continuum mechanics
ESAIM: M2AN, 39 4 (2005) 797-826
Published online: 2005-08-15
Articles citing this article
The Citing articles tool gives a list of articles citing the current article.
The citing articles come from EDP Sciences database, as well as other publishers participating in CrossRef Cited-by Linking Program. You can set up your personal account to receive an email alert each time this article is cited by a new article (see the menu on the right-hand side of the abstract page).
Cited article:
This article has been cited by the following article(s):
Uncertainty Quantification Guided Parameter Selection in a Fully Coupled Molecular Dynamics-Finite Element Model of the Mechanical Behavior of Polymers
Yunfeng Mao, Alf Gerisch, Jens Lang, Michael C. Böhm and Florian Müller-PlatheJournal of Chemical Theory and Computation 17 (6) 3760 (2021)
https://doi.org/10.1021/acs.jctc.0c01348
Homogenization of a one-dimensional diffusion - discrete absorption equation with feedback
Grigory Panasenko and Vitaly VolpertApplicable Analysis 95 (7) 1507 (2016)
https://doi.org/10.1080/00036811.2016.1179288
A Theoretical Examination of Diffusive Molecular Dynamics
G. Simpson, M. Luskin and D. J. SrolovitzSIAM Journal on Applied Mathematics 76 (6) 2175 (2016)
https://doi.org/10.1137/15M1024858
On a $\Gamma$-Convergence Analysis of a Quasicontinuum Method
Mathias Schäffner and Anja SchlömerkemperMultiscale Modeling & Simulation 13 (1) 132 (2015)
https://doi.org/10.1137/140971439
Encyclopedia of Applied and Computational Mathematics
Mitchell Luskin and Christoph OrtnerEncyclopedia of Applied and Computational Mathematics 89 (2015)
https://doi.org/10.1007/978-3-540-70529-1_271
Analysis of Transition State Theory Rates upon Spatial Coarse-Graining
Andrew Binder, Mitchell Luskin, Danny Perez and Arthur F. VoterMultiscale Modeling & Simulation 13 (3) 890 (2015)
https://doi.org/10.1137/140983963
Theory-based benchmarking of the blended force-based quasicontinuum method
Xingjie Helen Li, Mitchell Luskin, Christoph Ortner and Alexander V. ShapeevComputer Methods in Applied Mechanics and Engineering 268 763 (2014)
https://doi.org/10.1016/j.cma.2013.10.007
Lattice stability for atomistic chains modeled by local approximations of the embedded atom method
Xingjie Helen Li and Mitchell LuskinComputational Materials Science 66 96 (2013)
https://doi.org/10.1016/j.commatsci.2012.04.038
Atomistic-to-continuum coupling
Mitchell Luskin and Christoph OrtnerActa Numerica 22 397 (2013)
https://doi.org/10.1017/S0962492913000068
Atomistic-to-Continuum Coupling Approximation of a One-Dimensional Toy Model for Density Functional Theory
B. Langwallner, C. Ortner and E. SüliMultiscale Modeling & Simulation 11 (1) 59 (2013)
https://doi.org/10.1137/110857787
Finite Element Analysis of Cauchy–Born Approximations to Atomistic Models
Charalambos Makridakis and Endre SüliArchive for Rational Mechanics and Analysis 207 (3) 813 (2013)
https://doi.org/10.1007/s00205-012-0582-8
Partial asymptotic decomposition of the domain for the diffusion-discrete absorption equation
G. P. PanasenkoProceedings of the Steklov Institute of Mathematics 281 (S1) 118 (2013)
https://doi.org/10.1134/S0081543813050118
A numerical strategy for coarse-graining two-dimensional atomistic models at finite temperature: The membrane case
X. Blanc and F. LegollComputational Materials Science 66 84 (2013)
https://doi.org/10.1016/j.commatsci.2012.04.045
About an analytical verification of quasi-continuum methods with Γ-convergence techniques
Mathias Schäffner and Anja SchlömerkemperMRS Proceedings 1535 (2013)
https://doi.org/10.1557/opl.2013.458
An analysis of the boundary layer in the 1D surface Cauchy–Born model
Kavinda Jayawardana, Christelle Mordacq, Christoph Ortner and Harold S. ParkESAIM: Mathematical Modelling and Numerical Analysis 47 (1) 109 (2013)
https://doi.org/10.1051/m2an/2012021
Positive Definiteness of the Blended Force-Based Quasicontinuum Method
Xingjie Helen Li, Mitchell Luskin and Christoph OrtnerMultiscale Modeling & Simulation 10 (3) 1023 (2012)
https://doi.org/10.1137/110859270
Numerical Analysis of Multiscale Computations
Mitchell Luskin and Christoph OrtnerLecture Notes in Computational Science and Engineering, Numerical Analysis of Multiscale Computations 82 331 (2012)
https://doi.org/10.1007/978-3-642-21943-6_14
Asymptotic numerical analysis of the diffusion‐discrete absorption equation
P. Kurbatova, G. Panasenko and V. VolpertMathematical Methods in the Applied Sciences 35 (4) 438 (2012)
https://doi.org/10.1002/mma.1572
83 67 (2012)
https://doi.org/10.1007/978-3-642-22061-6_3
Analysis of the Quasi-Nonlocal Approximation of Linear and Circular Chains in the Plane
Pavel Bělík and Mitchell LuskinMultiscale Modeling & Simulation 9 (4) 1495 (2011)
https://doi.org/10.1137/100806242
BOUNDARY LAYER ENERGIES FOR NONCONVEX DISCRETE SYSTEMS
LUCIA SCARDIA, ANJA SCHLÖMERKEMPER and CHIARA ZANINIMathematical Models and Methods in Applied Sciences 21 (04) 777 (2011)
https://doi.org/10.1142/S0218202511005210
Analysis of Energy-Based Blended Quasi-Continuum Approximations
Brian Van Koten and Mitchell LuskinSIAM Journal on Numerical Analysis 49 (5) 2182 (2011)
https://doi.org/10.1137/10081071X
Iterative methods for the force-based quasicontinuum approximation: Analysis of a 1D model problem
M. Dobson, M. Luskin and C. OrtnerComputer Methods in Applied Mechanics and Engineering 200 (37-40) 2697 (2011)
https://doi.org/10.1016/j.cma.2010.07.008
Non-local energetics of random heterogeneous lattices
Jan Zeman, Ron H.J. Peerlings and Marc G.D. GeersJournal of the Mechanics and Physics of Solids 59 (6) 1214 (2011)
https://doi.org/10.1016/j.jmps.2011.03.006
Finite-Temperature Coarse-Graining of One-Dimensional Models: Mathematical Analysis and Computational Approaches
X. Blanc, C. Le Bris, F. Legoll and C. PatzJournal of Nonlinear Science 20 (2) 241 (2010)
https://doi.org/10.1007/s00332-009-9057-y
Stability, Instability, and Error of the Force-based Quasicontinuum Approximation
Matthew Dobson, Mitchell Luskin and Christoph OrtnerArchive for Rational Mechanics and Analysis 197 (1) 179 (2010)
https://doi.org/10.1007/s00205-009-0276-z
Accuracy of quasicontinuum approximations near instabilities
M. Dobson, M. Luskin and C. OrtnerJournal of the Mechanics and Physics of Solids 58 (10) 1741 (2010)
https://doi.org/10.1016/j.jmps.2010.06.011
Sharp Stability Estimates for the Force-Based Quasicontinuum Approximation of Homogeneous Tensile Deformation
M. Dobson, M. Luskin and C. OrtnerMultiscale Modeling & Simulation 8 (3) 782 (2010)
https://doi.org/10.1137/090767005
Analysis of a One-Dimensional Nonlocal Quasi-Continuum Method
Pingbing Ming and Jerry Zhijian YangMultiscale Modeling & Simulation 7 (4) 1838 (2009)
https://doi.org/10.1137/080725842
An analysis of the effect of ghost force oscillation on quasicontinuum error
Matthew Dobson and Mitchell LuskinESAIM: Mathematical Modelling and Numerical Analysis 43 (3) 591 (2009)
https://doi.org/10.1051/m2an/2009007
Harnack Inequalities and Discrete—Continuous Error Estimates for a Chain of Atoms with Two—Body Interactions
R. Benguria, J. Dolbeault and R. MonneauJournal of Statistical Physics 134 (1) 27 (2009)
https://doi.org/10.1007/s10955-008-9662-4
An Optimal Order Error Analysis of the One-Dimensional Quasicontinuum Approximation
Matthew Dobson and Mitchell LuskinSIAM Journal on Numerical Analysis 47 (4) 2455 (2009)
https://doi.org/10.1137/08073723X
Iterative Solution of the Quasicontinuum Equilibrium Equations with Continuation
Matthew Dobson and Mitchell LuskinJournal of Scientific Computing 37 (1) 19 (2008)
https://doi.org/10.1007/s10915-008-9208-6
Asymptotic expansions by Γ-convergence
Andrea Braides and Lev TruskinovskyContinuum Mechanics and Thermodynamics 20 (1) 21 (2008)
https://doi.org/10.1007/s00161-008-0072-2
Connecting Atomistic-to-Continuum Coupling and Domain Decomposition
Michael L. Parks, Pavel B. Bochev and Richard B. LehoucqMultiscale Modeling & Simulation 7 (1) 362 (2008)
https://doi.org/10.1137/070682848
On Atomistic-to-Continuum Coupling by Blending
Santiago Badia, Michael Parks, Pavel Bochev, Max Gunzburger and Richard LehoucqMultiscale Modeling & Simulation 7 (1) 381 (2008)
https://doi.org/10.1137/07069969X
Error Estimation and Atomistic-Continuum Adaptivity for the Quasicontinuum Approximation of a Frenkel–Kontorova Model
Marcel Arndt and Mitchell LuskinMultiscale Modeling & Simulation 7 (1) 147 (2008)
https://doi.org/10.1137/070688559
Analysis of a force-based quasicontinuum approximation
Matthew Dobson and Mitchell LuskinESAIM: Mathematical Modelling and Numerical Analysis 42 (1) 113 (2008)
https://doi.org/10.1051/m2an:2007058
Goal-oriented adaptive mesh refinement for the quasicontinuum approximation of a Frenkel-Kontorova model
Marcel Arndt and Mitchell LuskinComputer Methods in Applied Mechanics and Engineering 197 (49-50) 4298 (2008)
https://doi.org/10.1016/j.cma.2008.05.005
Partial homogenization of discrete models
M. Betoue Etoughe and G. PanasenkoApplicable Analysis 87 (12) 1425 (2008)
https://doi.org/10.1080/00036810802378638
(2007)
https://doi.org/10.2514/6.2007-2314
Hybrid Continuum Mechanics and Atomistic Methods for Simulating Materials Deformation and Failure
Ronald E. Miller and Ellad B. TadmorMRS Bulletin 32 (11) 920 (2007)
https://doi.org/10.1557/mrs2007.189
Convergence Analysis of a Quasi‐Continuum Approximation for a Two‐Dimensional Material Without Defects
Ping LinSIAM Journal on Numerical Analysis 45 (1) 313 (2007)
https://doi.org/10.1137/050636772
Atomistic to Continuum limits for computational materials science
Xavier Blanc, Claude Le Bris and Pierre-Louis LionsESAIM: Mathematical Modelling and Numerical Analysis 41 (2) 391 (2007)
https://doi.org/10.1051/m2an:2007018
Analysis of a Prototypical Multiscale Method Coupling Atomistic and Continuum Mechanics: the Convex Case
Xavier Blanc, Claude Le Bris and Frédéric LegollActa Mathematicae Applicatae Sinica, English Series 23 (2) 209 (2007)
https://doi.org/10.1007/s10255-007-0364-5