-
1
-
-
33744782338
-
Derivation of higher order gradient continuum models from atomistic models for crystalline solids
-
M. ARNDT and M. GRIEBEL, Derivation of higher order gradient continuum models from atomistic models for crystalline solids, Multiscale Model. Simul., 4 (2005), pp. 531-562.
-
(2005)
Multiscale Model. Simul
, vol.4
, pp. 531-562
-
-
ARNDT, M.1
GRIEBEL, M.2
-
2
-
-
0039896302
-
Algebraic theory of multiplicative Schwarz methods
-
M. BENZI, A. FROMMER, R. NABBEN, and D. B. SZYLD, Algebraic theory of multiplicative Schwarz methods, Numer. Math., 89 (2001), pp. 605-639.
-
(2001)
Numer. Math
, vol.89
, pp. 605-639
-
-
BENZI, M.1
FROMMER, A.2
NABBEN, R.3
SZYLD, D.B.4
-
3
-
-
29844453809
-
Continuum limit for three-dimensional mass-spring networks and discrete Korn's inequality
-
M. BEREZHNYY and L. BERLYAND, Continuum limit for three-dimensional mass-spring networks and discrete Korn's inequality, J. Mech. Phys. Solids, 54 (2006), pp. 635-669.
-
(2006)
J. Mech. Phys. Solids
, vol.54
, pp. 635-669
-
-
BEREZHNYY, M.1
BERLYAND, L.2
-
4
-
-
0042403046
-
Multiplicative and additive Schwarz methods: Convergence in the two-domain case
-
T. Chan, R. Glowinski, J. Périaux, and O. Widlund, eds, SIAM, Philadelphia
-
P. E. BJøRSTAD, Multiplicative and additive Schwarz methods: Convergence in the two-domain case, in Domain Decomposition Methods, T. Chan, R. Glowinski, J. Périaux, and O. Widlund, eds., SIAM, Philadelphia, 1989, pp. 147-159.
-
(1989)
Domain Decomposition Methods
, pp. 147-159
-
-
BJøRSTAD, P.E.1
-
5
-
-
25444509289
-
Analysis of a prototypical multiscale method coupling atomistic and continuum mechanics
-
X. BLANC, C. LE BRIS, and F. LEGOLL, Analysis of a prototypical multiscale method coupling atomistic and continuum mechanics, M2AN Math. Model. Numer. Anal., 39 (2005), pp. 797-826.
-
(2005)
M2AN Math. Model. Numer. Anal
, vol.39
, pp. 797-826
-
-
BLANC, X.1
LE BRIS, C.2
LEGOLL, F.3
-
6
-
-
0035981342
-
From molecular models to continuum mechanics
-
X. BLANC, C. LE BRIS, and P.-L. LIONS, From molecular models to continuum mechanics, Arch. Ration. Mech. Anal., 164 (2002), pp. 341-381.
-
(2002)
Arch. Ration. Mech. Anal
, vol.164
, pp. 341-381
-
-
BLANC, X.1
LE BRIS, C.2
LIONS, P.-L.3
-
8
-
-
0003391447
-
-
4th ed, John Wiley and Sons, New York
-
R. D. COOK, D. S. MALKUS, M. E. PLESHA, and R. J. WITT, Concepts and Applications of Finite Element Analysis, 4th ed., John Wiley and Sons, New York, 2002.
-
(2002)
Concepts and Applications of Finite Element Analysis
-
-
COOK, R.D.1
MALKUS, D.S.2
PLESHA, M.E.3
WITT, R.J.4
-
9
-
-
0038579633
-
Atomistic/continuum coupling methods in multi-scale materials modeling
-
W. CURTIN and R. MILLER, Atomistic/continuum coupling methods in multi-scale materials modeling, Modell. Simul. Mater. Sci. Eng., 11 (2003), pp. R33-R68.
-
(2003)
Modell. Simul. Mater. Sci. Eng
, vol.11
-
-
CURTIN, W.1
MILLER, R.2
-
10
-
-
0037058026
-
A dynamic atomistic-continuum method for the simulation of crystalline materials
-
W. E and Z. HUANG, A dynamic atomistic-continuum method for the simulation of crystalline materials, J. Comput. Phys., 182 (2002), pp. 234-261.
-
(2002)
J. Comput. Phys
, vol.182
, pp. 234-261
-
-
WEINAN, E.1
HUANG, Z.2
-
11
-
-
85115955160
-
Analysis of the local quasicontinuum method
-
T. Li and P. Zhang, eds, Higher Education Press, Beijing
-
W. E and P. B. MING, Analysis of the local quasicontinuum method, in Frontiers and Prospects of Contemporary Applied Mathematics, T. Li and P. Zhang, eds., Higher Education Press, Beijing, 2005, pp. 18-32.
-
(2005)
Frontiers and Prospects of Contemporary Applied Mathematics
, pp. 18-32
-
-
WEINAN, E.1
MING, P.B.2
-
12
-
-
0002162989
-
The Cauchy and Born hypotheses for crystals
-
Academic Press, Orlando, FL
-
J. L. ERICKSEN, The Cauchy and Born hypotheses for crystals, in Phase Transformations and Material Instabilities in Solids, Academic Press, Orlando, FL, 1984, pp. 61-77.
-
(1984)
Phase Transformations and Material Instabilities in Solids
, pp. 61-77
-
-
ERICKSEN, J.L.1
-
13
-
-
33750993211
-
Bridging the scales in nano engineering and science
-
J. FISH, Bridging the scales in nano engineering and science, J. Nanopart. Res., 8 (2006), pp. 577-594.
-
(2006)
J. Nanopart. Res
, vol.8
, pp. 577-594
-
-
FISH, J.1
-
14
-
-
34247211693
-
Optimized Schwarz methods
-
M. J. GANDER, Optimized Schwarz methods, SIAM J. Numer. Anal., 44 (2006), pp. 699-731.
-
(2006)
SIAM J. Numer. Anal
, vol.44
, pp. 699-731
-
-
GANDER, M.J.1
-
15
-
-
0001623257
-
Hybrid atomistic-continuum formulations and the moving contactline problem
-
N. G. HADJICONSTANTINOU, Hybrid atomistic-continuum formulations and the moving contactline problem, J. Comput. Phys., 154 (1999), pp. 245-265.
-
(1999)
J. Comput. Phys
, vol.154
, pp. 245-265
-
-
HADJICONSTANTINOU, N.G.1
-
16
-
-
31144448186
-
Discussion of recent developments in hybrid atomistic-continuum methods for multiscale hydrodynamics
-
N. G. HADJICONSTANTINOU, Discussion of recent developments in hybrid atomistic-continuum methods for multiscale hydrodynamics, Bull. Pol. Acad. Sci., 53 (2005), pp. 335-342.
-
(2005)
Bull. Pol. Acad. Sci
, vol.53
, pp. 335-342
-
-
HADJICONSTANTINOU, N.G.1
-
18
-
-
0035451516
-
An analysis of the quasicontinuum method
-
J. KNAP and M. ORTIZ, An analysis of the quasicontinuum method, J. Mech. Phys. Solids, 49 (2001), pp. 1899-1923.
-
(2001)
J. Mech. Phys. Solids
, vol.49
, pp. 1899-1923
-
-
KNAP, J.1
ORTIZ, M.2
-
19
-
-
0026237358
-
-
Philos. Mag. A, 64
-
S. KOHLHOFF, P. GUMBSCH, and H. F. F ISCHMEISTER, Crack propagation in b.c.c. crystals studied with a combined finite-element and atomistic model, Philos. Mag. A, 64 (1991), pp. 851-878.
-
(1991)
Crack propagation in b.c.c. crystals studied with a combined finite-element and atomistic model
, pp. 851-878
-
-
KOHLHOFF, S.1
GUMBSCH, P.2
ISCHMEISTER, H.F.F.3
-
21
-
-
0002246664
-
Coupling continuum to molecular-dynamics simulation: Reflecting particle method and the field estimator
-
J. LI, D. LIAO, and S. YIP, Coupling continuum to molecular-dynamics simulation: Reflecting particle method and the field estimator, Phys. Rev. E (3), 57 (1998), pp. 7259-7267.
-
(1998)
Phys. Rev. E
, vol.57
, Issue.3
, pp. 7259-7267
-
-
LI, J.1
LIAO, D.2
YIP, S.3
-
22
-
-
0032591725
-
-
J. LI, D. LIAO, and S. YIP, Imposing field boundary conditions in MD simulation of fluids: Optimal particle controller and buffer zone feedback, in Multiscale Modeling of Materials, Mater. Res. Soc. Symp. Proc. 538, T. Diaz de la Rubia, T. Kaxiras, V. Bulatov, N. Ghoniem, and R. Phillips, eds., Materials Research Society, Warrendale, PA, 1999, pp. 473-478.
-
J. LI, D. LIAO, and S. YIP, Imposing field boundary conditions in MD simulation of fluids: Optimal particle controller and buffer zone feedback, in Multiscale Modeling of Materials, Mater. Res. Soc. Symp. Proc. 538, T. Diaz de la Rubia, T. Kaxiras, V. Bulatov, N. Ghoniem, and R. Phillips, eds., Materials Research Society, Warrendale, PA, 1999, pp. 473-478.
-
-
-
-
23
-
-
0033316545
-
Nearly exact solution for coupled continuum/MD fluid simulation
-
J. LI, D. LIAO, and S. YIP, Nearly exact solution for coupled continuum/MD fluid simulation, J. Computer Aided Mater. Des., 6 (1999), pp. 95-102.
-
(1999)
J. Computer Aided Mater. Des
, vol.6
, pp. 95-102
-
-
LI, J.1
LIAO, D.2
YIP, S.3
-
24
-
-
0037376075
-
Theoretical and numerical analysis for the quasi-continuum approximation of a material particle model
-
P. LIN, Theoretical and numerical analysis for the quasi-continuum approximation of a material particle model, Math. Comp., 72 (2003), pp. 657-675.
-
(2003)
Math. Comp
, vol.72
, pp. 657-675
-
-
LIN, P.1
-
25
-
-
36649017836
-
Convergence analysis of a quasi-continuum approximation for a two-dimensional material without defects
-
P. LIN, Convergence analysis of a quasi-continuum approximation for a two-dimensional material without defects, SIAM J. Numer. Anal., 45 (2007), pp. 313-332.
-
(2007)
SIAM J. Numer. Anal
, vol.45
, pp. 313-332
-
-
LIN, P.1
-
26
-
-
24144457619
-
Overview of multiscale simulations of materials, in Handbook of Theoretical and Computational Nanotechnology
-
X, M. Rieth and W. Schommers, eds, CA
-
G. LU and E. KAXIRAS, Overview of multiscale simulations of materials, in Handbook of Theoretical and Computational Nanotechnology, Vol. X, M. Rieth and W. Schommers, eds., American Scientific Publishers, Stevenson Ranch, CA, 2005, pp. 1-33.
-
(2005)
American Scientific Publishers, Stevenson Ranch
, pp. 1-33
-
-
LU, G.1
KAXIRAS, E.2
-
27
-
-
0242367374
-
The quasicontinuum method: Overview, applications, and current directions
-
R. E. MILLER and E. B. TADMOR, The quasicontinuum method: Overview, applications, and current directions, J. Computer Aided Mater. Des., 9 (2002), pp. 203-239.
-
(2002)
J. Computer Aided Mater. Des
, vol.9
, pp. 203-239
-
-
MILLER, R.E.1
TADMOR, E.B.2
-
28
-
-
85124574810
-
-
X. B. NIE, S. Y. CHEN, W. E, and M. O. ROBBINS, A continuum and molecular dynamics hybrid method for micro- and nano-fluid flow, J. Fluid Mech., 500 (2004), pp. 55-64.
-
X. B. NIE, S. Y. CHEN, W. E, and M. O. ROBBINS, A continuum and molecular dynamics hybrid method for micro- and nano-fluid flow, J. Fluid Mech., 500 (2004), pp. 55-64.
-
-
-
-
29
-
-
7244258908
-
Hybrid continuum-atomistic simulation of singular corner flow
-
X. B. NIE, S. Y. CHEN, and M. O. ROBBINS, Hybrid continuum-atomistic simulation of singular corner flow, Phys. Fluids, 15 (2004), pp. 3579-3591.
-
(2004)
Phys. Fluids
, vol.15
, pp. 3579-3591
-
-
NIE, X.B.1
CHEN, S.Y.2
ROBBINS, M.O.3
-
30
-
-
1842809898
-
An introduction and tutorial of multiple-scale analysis in solids
-
H. S. PARK and W. K. LIU, An introduction and tutorial of multiple-scale analysis in solids, Comput. Methods Appl. Mech. Engrg., 193 (2004), pp. 1733-1772.
-
(2004)
Comput. Methods Appl. Mech. Engrg
, vol.193
, pp. 1733-1772
-
-
PARK, H.S.1
LIU, W.K.2
-
32
-
-
55249117659
-
-
H. A. SCHWARZ, Gesammelete Mathematische Abhandlungen, 2, Springer, Berlin, 1890, pp. 133-143. First published in Vierteljahrsschrift der Naturforschenden Gesellschaft in Zürich, 15 (1870), pp. 272-286.
-
H. A. SCHWARZ, Gesammelete Mathematische Abhandlungen, Vol. 2, Springer, Berlin, 1890, pp. 133-143. First published in Vierteljahrsschrift der Naturforschenden Gesellschaft in Zürich, 15 (1870), pp. 272-286.
-
-
-
-
33
-
-
0033100627
-
An adaptive finite element approach to atomic-scale mechanics-The quasicontinuum method
-
V. B. SHENOY, R. MILLER, E. B. TADMOR, D. RODNEY, R. PHILLIPS, and M. ORTIZ, An adaptive finite element approach to atomic-scale mechanics-The quasicontinuum method, J. Mech. Phys. Solids, 47 (1999), pp. 611-642.
-
(1999)
J. Mech. Phys. Solids
, vol.47
, pp. 611-642
-
-
SHENOY, V.B.1
MILLER, R.2
TADMOR, E.B.3
RODNEY, D.4
PHILLIPS, R.5
ORTIZ, M.6
-
34
-
-
0003419897
-
-
Cambridge University Press, Cambridge, UK
-
B. SMITH, P. E. BJøRSTAD, and W. GROPP, Domain Decomposition: Parallel Multilevel Methods for Elliptic Partial Differential Equations, Cambridge University Press, Cambridge, UK, 1999.
-
(1999)
Domain Decomposition: Parallel Multilevel Methods for Elliptic Partial Differential Equations
-
-
SMITH, B.1
BJøRSTAD, P.E.2
GROPP, W.3
-
35
-
-
0003552714
-
An Analysis of the Finite Element Method
-
Prentice-Hall, Englewood Cliffs, NJ
-
G. STRANG and G. J. FIX, An Analysis of the Finite Element Method, Prentice-Hall Series in Automatic Computation, Prentice-Hall, Englewood Cliffs, NJ, 1973.
-
(1973)
Prentice-Hall Series in Automatic Computation
-
-
STRANG, G.1
FIX, G.J.2
-
36
-
-
0030158774
-
Quasicontinuum analysis of defects in solids
-
E. B. TADMOR, M. ORTIZ, and R. PHILLIPS, Quasicontinuum analysis of defects in solids, Philos. Mag. A, 73 (1996), pp. 1529-1563.
-
(1996)
Philos. Mag. A
, vol.73
, pp. 1529-1563
-
-
TADMOR, E.B.1
ORTIZ, M.2
PHILLIPS, R.3
-
37
-
-
55249099036
-
A combined atomistic/continuum analysis of nanoelectromechanical systems
-
San Francisco, IEEE Press, New York
-
Z. TANG and N. R. ALURU, A combined atomistic/continuum analysis of nanoelectromechanical systems, in IEEE-NANO 2003, Third IEEE Conference on Nanotechnology, Vol. 2, San Francisco, 2003, IEEE Press, New York, 2003, pp. 191-194.
-
(2003)
IEEE-NANO 2003, Third IEEE Conference on Nanotechnology
, vol.2
, pp. 191-194
-
-
TANG, Z.1
ALURU, N.R.2
-
38
-
-
11144335525
-
Multiscale modelling of nanostructures
-
D. D. VVEDENSKY, Multiscale modelling of nanostructures, J. Phys.: Condens. Matter, 16 (2004), pp. R1537-R1576.
-
(2004)
J. Phys.: Condens. Matter
, vol.16
-
-
VVEDENSKY, D.D.1
-
39
-
-
16844364042
-
Hybrid atomistic-continuum method for the simulation of dense fluid flows
-
T. WERDER, J. H. WALTHER, and P. KOUMOUTSAKOS, Hybrid atomistic-continuum method for the simulation of dense fluid flows, J. Comput. Phys., 205 (2005), pp. 373-290.
-
(2005)
J. Comput. Phys
, vol.205
, pp. 373-290
-
-
WERDER, T.1
WALTHER, J.H.2
KOUMOUTSAKOS, P.3
-
40
-
-
24144458425
-
Discussion of hybrid atomistic-continuum methods for multiscale hydrodynamics
-
H. S. WIJESINGHE and N. G. HADJICONSTANTINOU, Discussion of hybrid atomistic-continuum methods for multiscale hydrodynamics, Internat. J. Mult. Comp. Eng., 2 (2004), pp. 189-202.
-
(2004)
Internat. J. Mult. Comp. Eng
, vol.2
, pp. 189-202
-
-
WIJESINGHE, H.S.1
HADJICONSTANTINOU, N.G.2
|