-
1
-
-
34547343685
-
Subgrid upscaling and mixed multiscale finite elements
-
10.1137/050631811
-
Todd Arbogast, and Kirsten J. Boyd Subgrid upscaling and mixed multiscale finite elements SIAM J. Numer. Anal. 44 2006 1150 1171 10.1137/050631811
-
(2006)
SIAM J. Numer. Anal.
, vol.44
, pp. 1150-1171
-
-
Arbogast, T.1
Boyd, K.J.2
-
3
-
-
0029656559
-
On the Hamiltonian balanced dynamics and the slowest invariant manifold
-
10.1175/1520-0469(1996)053!0276:OHBDAT?2.0.CO;2
-
O. Bokhove, and T.G. Shepherd On the Hamiltonian balanced dynamics and the slowest invariant manifold J. Atmos. Sci. 53 2 1996 276 297 10.1175/1520-0469(1996)053!0276:OHBDAT?2.0.CO;2
-
(1996)
J. Atmos. Sci.
, vol.53
, Issue.2
, pp. 276-297
-
-
Bokhove, O.1
Shepherd, T.G.2
-
5
-
-
0142014324
-
General highly accurate algebraic coarsening
-
Achi Brandt General highly accurate algebraic coarsening Elect. Trans. Num. Anal. 10 2000 1 20 http://www.emis.ams.org/journals/ETNA/vol.10.2000/pp1- 20.dir/pp1-20.html
-
(2000)
Elect. Trans. Num. Anal.
, vol.10
, pp. 1-20
-
-
Brandt, A.1
-
7
-
-
67649493209
-
-
Achi Brandt Methods of systematic upscaling Technical report, Department of Computer Science and Applied Mathematics, The Weizmann Institute of Science, March 2006 http://wisdomarchive.wisdom.weizmann.ac.il:81/archive/00000398/
-
Methods of Systematic Upscaling
-
-
Brandt, A.1
-
9
-
-
0003289290
-
Applications of Centre Manifold Theory
-
Springer-Verlag
-
J. Carr Applications of Centre Manifold Theory Applied Math. Sci. vol. 35 1981 Springer-Verlag
-
(1981)
Applied Math. Sci.
, vol.35
-
-
Carr, J.1
-
10
-
-
1542471855
-
Lattice Boltzmann method for fluid flows
-
10.1146/annurev.fluid.30.1.329
-
Chen Shiyi, and G.D. Doolen Lattice Boltzmann method for fluid flows Annu. Rev. Fluid Mechanics 30 1998 329 364 10.1146/annurev.fluid.30.1.329
-
(1998)
Annu. Rev. Fluid Mechanics
, vol.30
, pp. 329-364
-
-
Shiyi, C.1
Doolen, G.D.2
-
12
-
-
12044252828
-
Pattern formation outside of equilibrium
-
10.1103/RevModPhys.65.851
-
M.C. Cross, and P.C. Hohenberg Pattern formation outside of equilibrium Rev. Mod. Phys. 65 3 1993 851 1112 10.1103/RevModPhys.65.851
-
(1993)
Rev. Mod. Phys.
, vol.65
, Issue.3
, pp. 851-1112
-
-
Cross, M.C.1
Hohenberg, P.C.2
-
15
-
-
0001157761
-
On the computation of inertial manifolds
-
10.1016/0375-9601(88)90295-2
-
C. Foias, M.S. Jolly, I.G. Kevrekidis, G.R. Sell, and E.S. Titi On the computation of inertial manifolds Phys. Lett. A 131 1988 433 436 10.1016/0375-9601(88)90295-2
-
(1988)
Phys. Lett. A
, vol.131
, pp. 433-436
-
-
Foias, C.1
Jolly, M.S.2
Kevrekidis, I.G.3
Sell, G.R.4
Titi, E.S.5
-
16
-
-
0000166593
-
Determining nodes, finite difference schemes and inertial manifolds
-
10.1088/0951-7715/4/1/009
-
C. Foias, and E.S. Titi Determining nodes, finite difference schemes and inertial manifolds Nonlinearity 4 1991 135 153 10.1088/0951-7715/4/1/009
-
(1991)
Nonlinearity
, vol.4
, pp. 135-153
-
-
Foias, C.1
Titi, E.S.2
-
17
-
-
21144468600
-
A center-stable manifold theorem for differential equations in Banach spaces
-
Th. Gallay A center-stable manifold theorem for differential equations in Banach spaces Commun. Math. Phys 152 1993 249 268
-
(1993)
Commun. Math. Phys
, vol.152
, pp. 249-268
-
-
Gallay, T.1
-
18
-
-
0032206010
-
Space-time continuous analysis of waveform relaxation for the heat equation
-
Martin J. Gander, and Andrew M. Stuart Space-time continuous analysis of waveform relaxation for the heat equation SIAM J. Scientific Computing 19 6 1998 2014 2031
-
(1998)
SIAM J. Scientific Computing
, vol.19
, Issue.6
, pp. 2014-2031
-
-
Gander, M.J.1
Stuart, A.M.2
-
19
-
-
17344387998
-
The gap-tooth method in particle simulations
-
10.1016/j.physleta.2003.07.004
-
C.W. Gear, Ju Li, and I.G. Kevrekidis The gap-tooth method in particle simulations Phys. Lett. A 316 2003 190 195 10.1016/j.physleta.2003.07.004
-
(2003)
Phys. Lett. A
, vol.316
, pp. 190-195
-
-
Gear, C.W.1
Li, J.2
Kevrekidis, I.G.3
-
21
-
-
34047228827
-
Approximate inertial manifolds for the Kuramoto-Sivashinsky equation: Analysis and computations
-
10.1016/0167-2789(90)90046-R
-
M.S. Jolly, I.G. Kevrekidis, and E.S. Titi Approximate inertial manifolds for the Kuramoto-Sivashinsky equation: analysis and computations Physica D 44 1990 38 60 10.1016/0167-2789(90)90046-R
-
(1990)
Physica D
, vol.44
, pp. 38-60
-
-
Jolly, M.S.1
Kevrekidis, I.G.2
Titi, E.S.3
-
22
-
-
85128858890
-
Equation-free, coarse-grained multiscale computation: Enabling microscopic simulators to perform system level tasks
-
I.G. Kevrekidis, C.W. Gear, J.M. Hyman, P.G. Kevrekidis, O. Runborg, and K. Theodoropoulos Equation-free, coarse-grained multiscale computation: enabling microscopic simulators to perform system level tasks Comm. Math. Sciences 1 2003 715 762
-
(2003)
Comm. Math. Sciences
, vol.1
, pp. 715-762
-
-
Kevrekidis, I.G.1
Gear, C.W.2
Hyman, J.M.3
Kevrekidis, P.G.4
Runborg, O.5
Theodoropoulos, K.6
-
23
-
-
0347987814
-
New high-resolution central schemes for nonlinear conservation laws and convection-diffusion equations
-
10.1006/jcph.2000.6459
-
Alexander Kurganov, and Eitan Tadmor New high-resolution central schemes for nonlinear conservation laws and convection-diffusion equations J. Computational Physics 160 2000 241 282 10.1006/jcph.2000.6459
-
(2000)
J. Computational Physics
, vol.160
, pp. 241-282
-
-
Kurganov, A.1
Tadmor, E.2
-
24
-
-
0003236870
-
Elements of Applied Bifurcation Theory
-
Springer-Verlag
-
Y.A. Kuznetsov Elements of Applied Bifurcation Theory Applied Mathematical Sciences vol. 112 1995 Springer-Verlag
-
(1995)
Applied Mathematical Sciences
, vol.112
-
-
Kuznetsov, Y.A.1
-
26
-
-
57249110723
-
Accurately model the Kuramoto-Sivashinsky dynamics with holistic discretisation
-
T. MacKenzie, and A.J. Roberts Accurately model the Kuramoto-Sivashinsky dynamics with holistic discretisation SIAM J. Applied Dynamical Systems 5 3 2006 365 402
-
(2006)
SIAM J. Applied Dynamical Systems
, vol.5
, Issue.3
, pp. 365-402
-
-
MacKenzie, T.1
Roberts, A.J.2
-
28
-
-
0000547750
-
Nonlinear Galerkin methods
-
M. Marion, and R. Temam Nonlinear Galerkin methods SIAM J. Numer. Anal. 26 5 1989 1139 1157 http://locus.siam.org/SINUM/volume-26/art-0726063.html
-
(1989)
SIAM J. Numer. Anal.
, vol.26
, Issue.5
, pp. 1139-1157
-
-
Marion, M.1
Temam, R.2
-
29
-
-
0025567096
-
A centre manifold description of contaminant dispersion in channels with varying flow properties
-
G.N. Mercer, and A.J. Roberts A centre manifold description of contaminant dispersion in channels with varying flow properties SIAM J. Appl. Math. 50 1990 1547 1565 http://link.aip.org/link/?SMM/50/1547/1
-
(1990)
SIAM J. Appl. Math.
, vol.50
, pp. 1547-1565
-
-
Mercer, G.N.1
Roberts, A.J.2
-
32
-
-
0000144318
-
The utility of an invariant manifold description of the evolution of a dynamical system
-
A.J. Roberts The utility of an invariant manifold description of the evolution of a dynamical system SIAM J. Math. Anal. 20 1989 1447 1458 http://locus.siam.org/SIMA/volume-20/art-0520094.html
-
(1989)
SIAM J. Math. Anal.
, vol.20
, pp. 1447-1458
-
-
Roberts, A.J.1
-
33
-
-
0031099492
-
Low-dimensional modelling of dynamics via computer algebra
-
10.1016/S0010-4655(96)00162-2
-
A.J. Roberts Low-dimensional modelling of dynamics via computer algebra Computer Phys. Comm. 100 1997 215 230 10.1016/S0010-4655(96)00162-2
-
(1997)
Computer Phys. Comm.
, vol.100
, pp. 215-230
-
-
Roberts, A.J.1
-
34
-
-
0035341644
-
Holistic discretisation ensures fidelity to Burgers' equation
-
10.1016/S0168-9274(00)00053-2
-
A.J. Roberts Holistic discretisation ensures fidelity to Burgers' equation Appl. Numer. Modelling 37 2001 371 396 10.1016/S0168-9274(00)00053-2
-
(2001)
Appl. Numer. Modelling
, vol.37
, pp. 371-396
-
-
Roberts, A.J.1
-
36
-
-
33644545273
-
Simple and fast multigrid solution of Poisson's equation using diagonally oriented grids
-
A.J. Roberts Simple and fast multigrid solution of Poisson's equation using diagonally oriented grids ANZIAM J. 43 E July 2001 E1 E36 http://anziamj.austms.org.au/ojs/index.php/ANZIAMJ/article/view/465
-
(2001)
ANZIAM J.
, vol.43
, Issue.E
-
-
Roberts, A.J.1
-
37
-
-
0037232578
-
A holistic finite difference approach models linear dynamics consistently
-
A.J. Roberts A holistic finite difference approach models linear dynamics consistently Mathematics of Computation 72 2002 247 262 http://www.ams.org/ mcom/2003-72-241/S0025-5718-02-01448-5
-
(2002)
Mathematics of Computation
, vol.72
, pp. 247-262
-
-
Roberts, A.J.1
-
38
-
-
77955559104
-
Derive boundary conditions for holistic discretisations of Burgers' equation
-
A.J. Roberts Derive boundary conditions for holistic discretisations of Burgers' equation K. Burrage, Roger B. Sidje, Proc. of 10th Computational Techniques and Applications Conference CTAC-2001 vol. 44 March 2003 C664 C686 http://anziamj.austms.org.au/ojs/index.php/ANZIAMJ/article/view/701
-
(2003)
Proc. of 10th Computational Techniques and Applications Conference CTAC-2001
, vol.44
-
-
Roberts, A.J.1
-
41
-
-
67649532603
-
Model dynamics across multiple length and time scales on a spatial multigrid
-
A.J. Roberts Model dynamics across multiple length and time scales on a spatial multigrid Multiscale Modeling and Simulation 7 4 2009 1525 1548
-
(2009)
Multiscale Modeling and Simulation
, vol.7
, Issue.4
, pp. 1525-1548
-
-
Roberts, A.J.1
-
42
-
-
48249118227
-
Higher order accuracy in the gap-tooth scheme for large-scale dynamics using microscopic simulators
-
ANZIAM J.
-
A.J. Roberts, and I.G. Kevrekidis Higher order accuracy in the gap-tooth scheme for large-scale dynamics using microscopic simulators Rob May, A.J. Roberts, Proc. of 12th Computational Techniques and Applications Conference CTAC-2004 ANZIAM J. vol. 46 July 2005 C637 C657 http://anziamj.austms.org.au/ V46/CTAC2004/Robe [July 20, 2005]
-
(2005)
Proc. of 12th Computational Techniques and Applications Conference CTAC-2004
, vol.46
-
-
Roberts, A.J.1
Kevrekidis, I.G.2
-
43
-
-
35748963495
-
General tooth boundary conditions for equation free modelling
-
10.1137/060654554
-
A.J. Roberts, and I.G. Kevrekidis General tooth boundary conditions for equation free modelling SIAM J. Scientific Computing 29 4 2007 1495 1510 10.1137/060654554
-
(2007)
SIAM J. Scientific Computing
, vol.29
, Issue.4
, pp. 1495-1510
-
-
Roberts, A.J.1
Kevrekidis, I.G.2
-
44
-
-
0000242930
-
The asymptotic completeness of inertial manifolds
-
J.C. Robinson The asymptotic completeness of inertial manifolds Nonlinearity 9 1996 1325 1340 http://www.iop.org/EJ/abstract/0951-7715/9/5/013
-
(1996)
Nonlinearity
, vol.9
, pp. 1325-1340
-
-
Robinson, J.C.1
-
46
-
-
84966201033
-
Properties of centre manifolds
-
J. Sijbrand Properties of centre manifolds Trans. Amer. Math. Soc. 289 1985 431 469
-
(1985)
Trans. Amer. Math. Soc.
, vol.289
, pp. 431-469
-
-
Sijbrand, J.1
-
47
-
-
34548103810
-
Simulating invasion with cellular automata: Connecting cell-scale and population-scale properties
-
10.1103/PhysRevE.76.021918
-
Matthew J. Simpson, Alistair Merrifield, Kerry A. Landman, and Barry D. Hughes Simulating invasion with cellular automata: Connecting cell-scale and population-scale properties Phys. Rev. E 76 2007 021918 10.1103/PhysRevE.76. 021918
-
(2007)
Phys. Rev. e
, vol.76
, pp. 021918
-
-
Simpson, M.J.1
Merrifield, A.2
Landman, K.A.3
Hughes, B.D.4
-
49
-
-
0344272168
-
Textbook multigrid efficiency for fluid simulations
-
10.1146/annurev.fluid.35.101101.161209
-
James L. Thomas, Boris Diskin, and Achi Brandt Textbook multigrid efficiency for fluid simulations Annu. Rev. Fluid Mechanics 35 2003 317 340 10.1146/annurev.fluid.35.101101.161209
-
(2003)
Annu. Rev. Fluid Mechanics
, vol.35
, pp. 317-340
-
-
Thomas, J.L.1
Diskin, B.2
Brandt, A.3
-
50
-
-
0000950086
-
Center manifold theory in infinite dimensions
-
A. Vanderbauwhede, and G. Iooss Center manifold theory in infinite dimensions Dynamics Reported 1 1988 125 163
-
(1988)
Dynamics Reported
, vol.1
, pp. 125-163
-
-
Vanderbauwhede, A.1
Iooss, G.2
-
51
-
-
0006144178
-
Self-similar asymptotics for linear and nonlinear diffusion equations
-
T.P. Witelski, and A.J. Bernoff Self-similar asymptotics for linear and nonlinear diffusion equations Studies in Applied Maths. 100 1998 153 193 http://www.ingentaconnect.com/content/bpl/sapm/1998/00000100/00000002/art00074
-
(1998)
Studies in Applied Maths.
, vol.100
, pp. 153-193
-
-
Witelski, T.P.1
Bernoff, A.J.2
-
52
-
-
0028449003
-
Weakly nonlinear analyses of prototype reaction-diffusion model equations
-
D.J. Wollkind, V.S. Manoranjan, and L. Zhang Weakly nonlinear analyses of prototype reaction-diffusion model equations SIAM Review 36 2 1994 176 214
-
(1994)
SIAM Review
, vol.36
, Issue.2
, pp. 176-214
-
-
Wollkind, D.J.1
Manoranjan, V.S.2
Zhang, L.3
|