-
1
-
-
0000325341
-
On lines and planes of closest fit to systems of points in space
-
Pearson K. On lines and planes of closest fit to systems of points in space. Philos. Mag. 1901, 2:559-572.
-
(1901)
Philos. Mag.
, vol.2
, pp. 559-572
-
-
Pearson, K.1
-
2
-
-
0002323798
-
Statistics in function space
-
Kosambi D.D. Statistics in function space. J. Indian Math. Soc. 1943, 7:76-88.
-
(1943)
J. Indian Math. Soc.
, vol.7
, pp. 76-88
-
-
Kosambi, D.D.1
-
5
-
-
4844222391
-
Strategies for model reduction: comparing different optimal bases
-
Crommelin D.T., Majda A.J. Strategies for model reduction: comparing different optimal bases. J. Atmos. Sci. 2004, 61:2206-2217.
-
(2004)
J. Atmos. Sci.
, vol.61
, pp. 2206-2217
-
-
Crommelin, D.T.1
Majda, A.J.2
-
6
-
-
84972308308
-
The dynamics of coherent structures in the wall region of a turbulent boundary layer
-
Aubry N., Holmes P., Lumley J.L. The dynamics of coherent structures in the wall region of a turbulent boundary layer. J. Fluid Dynam. 1998, 192:115-173.
-
(1998)
J. Fluid Dynam.
, vol.192
, pp. 115-173
-
-
Aubry, N.1
Holmes, P.2
Lumley, J.L.3
-
7
-
-
0038693394
-
Galerkin proper orthogonal decomposition methods for a general equation in fluid dynamics
-
Kunisch K., Volkwein S. Galerkin proper orthogonal decomposition methods for a general equation in fluid dynamics. SIAM J. Numer. Anal. 2003, 40:492-515.
-
(2003)
SIAM J. Numer. Anal.
, vol.40
, pp. 492-515
-
-
Kunisch, K.1
Volkwein, S.2
-
8
-
-
34547660515
-
Proper orthogonal decomposition approach and error estimation of mixed finite element methods for the tropical pacific ocean reduced gravity model
-
Luo Z., Zhu J., Wang R., Navon I.M. Proper orthogonal decomposition approach and error estimation of mixed finite element methods for the tropical pacific ocean reduced gravity model. Comput. Methods Appl. Mech. Engrg. 2007, 196:4184-4195.
-
(2007)
Comput. Methods Appl. Mech. Engrg.
, vol.196
, pp. 4184-4195
-
-
Luo, Z.1
Zhu, J.2
Wang, R.3
Navon, I.M.4
-
9
-
-
0002708045
-
The structure of inhomogeneous turbulence
-
Lumley J.L. The structure of inhomogeneous turbulence. Atmos. Turbul. Wave Propag. 1967, 166-178.
-
(1967)
Atmos. Turbul. Wave Propag.
, pp. 166-178
-
-
Lumley, J.L.1
-
10
-
-
84972308308
-
The dynamics of coherent structures in the wall region of a turbulent boundary layer
-
Aubry N., Holmes P., Lumley J.L. The dynamics of coherent structures in the wall region of a turbulent boundary layer. J. Fluid Dynam. 1988, 192:115-173.
-
(1988)
J. Fluid Dynam.
, vol.192
, pp. 115-173
-
-
Aubry, N.1
Holmes, P.2
Lumley, J.L.3
-
11
-
-
0036849510
-
Balanced model reduction via the proper orthogonal decomposition
-
Willcox K., Peraire J. Balanced model reduction via the proper orthogonal decomposition. AIAA J. 2002, 40:2323-2330.
-
(2002)
AIAA J.
, vol.40
, pp. 2323-2330
-
-
Willcox, K.1
Peraire, J.2
-
12
-
-
0001589981
-
Nondestructive evaluation using a reduced-order computational methodology
-
Banks H.T., Joyner M.L., Wincheski B., Winfree W.P. Nondestructive evaluation using a reduced-order computational methodology. Inverse Probl. 2000, 16:929-945.
-
(2000)
Inverse Probl.
, vol.16
, pp. 929-945
-
-
Banks, H.T.1
Joyner, M.L.2
Wincheski, B.3
Winfree, W.P.4
-
13
-
-
77954347097
-
Three-dimensional simulation and inversion of borehole temperatures for reconstructing past climate in complex settings
-
Hopcroftand P.O., Gallagher K., Pain C.C., Fang F. Three-dimensional simulation and inversion of borehole temperatures for reconstructing past climate in complex settings. J. Geophys. Res. 2009, 114.
-
(2009)
J. Geophys. Res.
, pp. 114
-
-
Hopcroftand, P.O.1
Gallagher, K.2
Pain, C.C.3
Fang, F.4
-
14
-
-
22744435478
-
A reduced-order strategy for 4D-Var data assimilation
-
Robert C., Durbiano S., Blayo E., Verron J., Blum J., Dimet F.X.L. A reduced-order strategy for 4D-Var data assimilation. J. Marine Syst. 2005, 57:70-82.
-
(2005)
J. Marine Syst.
, vol.57
, pp. 70-82
-
-
Robert, C.1
Durbiano, S.2
Blayo, E.3
Verron, J.4
Blum, J.5
Dimet, F.X.L.6
-
15
-
-
33947515129
-
A reduced order approach to four-dimensional variational data assimilation using proper orthogonal decomposition
-
Cao Y., Zhu J., Navon I.M., Luo Z. A reduced order approach to four-dimensional variational data assimilation using proper orthogonal decomposition. Int. J. Numer. Methods Fluids 2007, 53:1571-1583.
-
(2007)
Int. J. Numer. Methods Fluids
, vol.53
, pp. 1571-1583
-
-
Cao, Y.1
Zhu, J.2
Navon, I.M.3
Luo, Z.4
-
16
-
-
33746082025
-
Efficiency of reduced-order, time-dependent adjoint data assimilation approaches
-
Hoteit I., Kohl A. Efficiency of reduced-order, time-dependent adjoint data assimilation approaches. J. Oceanogr. 2006, 62:539-550.
-
(2006)
J. Oceanogr.
, vol.62
, pp. 539-550
-
-
Hoteit, I.1
Kohl, A.2
-
17
-
-
66149148365
-
Reduced order modelling of an adaptive mesh ocean model
-
Fang F., Pain C.C., Navon I.M., Piggott M.D., Gorman G.J., Allison P., Goddard A.J.H. Reduced order modelling of an adaptive mesh ocean model. Int. J. Numer. Methods Fluids 2009, 59:827-851.
-
(2009)
Int. J. Numer. Methods Fluids
, vol.59
, pp. 827-851
-
-
Fang, F.1
Pain, C.C.2
Navon, I.M.3
Piggott, M.D.4
Gorman, G.J.5
Allison, P.6
Goddard, A.J.H.7
-
18
-
-
0026928030
-
Stabilized finite element methods: II. The incompressible Navier-Stokes equations
-
Franca L.P., Frey S. Stabilized finite element methods: II. The incompressible Navier-Stokes equations. Comput. Methods Appl. Mech. Engrg. 1992, 99:209-233.
-
(1992)
Comput. Methods Appl. Mech. Engrg.
, vol.99
, pp. 209-233
-
-
Franca, L.P.1
Frey, S.2
-
19
-
-
84871658725
-
On the stability and convergence of a Galerkin reduced order model (ROM) of compressible flow with solid wall and far-field boundary treatment
-
Kalashnikova I., Barone M.F. On the stability and convergence of a Galerkin reduced order model (ROM) of compressible flow with solid wall and far-field boundary treatment. Int. J. Numer. Methods Engrg. 2009, 00:1-28.
-
(2009)
Int. J. Numer. Methods Engrg.
, vol.0
, pp. 1-28
-
-
Kalashnikova, I.1
Barone, M.F.2
-
20
-
-
0034400382
-
Stability properties of POD/Galerkin approximations for the compressible Navier-Stokes equations
-
Iollo A., Lanteri S., Desideri J.A. Stability properties of POD/Galerkin approximations for the compressible Navier-Stokes equations. Theor. Comput. Fluid Dynam. 2000, 13:377-396.
-
(2000)
Theor. Comput. Fluid Dynam.
, vol.13
, pp. 377-396
-
-
Iollo, A.1
Lanteri, S.2
Desideri, J.A.3
-
21
-
-
33845790413
-
Two stable POD-based approximations to the Navier-Stokes equations
-
Iollo A., Dervieux A., Desideri J.A., Lanteri S. Two stable POD-based approximations to the Navier-Stokes equations. Comput. Visual. Sci. 2000, 3:61-66.
-
(2000)
Comput. Visual. Sci.
, vol.3
, pp. 61-66
-
-
Iollo, A.1
Dervieux, A.2
Desideri, J.A.3
Lanteri, S.4
-
22
-
-
84655169928
-
α regularization of the POD-Galerkin dynamical systems of the Kuramoto-Sivashinsky equation
-
Sabetghadam F., Jafarpour A. α regularization of the POD-Galerkin dynamical systems of the Kuramoto-Sivashinsky equation. Appl. Math. Comput. 2012, 218:6012-6026.
-
(2012)
Appl. Math. Comput.
, vol.218
, pp. 6012-6026
-
-
Sabetghadam, F.1
Jafarpour, A.2
-
23
-
-
78149314237
-
Nonlinear model reduction via discrete empirical interpolation
-
Chaturantabut S., Sorensen D.C. Nonlinear model reduction via discrete empirical interpolation. SIAM J. Sci. Comput. 2010, 32:2737-2764.
-
(2010)
SIAM J. Sci. Comput.
, vol.32
, pp. 2737-2764
-
-
Chaturantabut, S.1
Sorensen, D.C.2
-
24
-
-
15744385841
-
An empirical interpolation method: application to efficient reduced-basis discretization of partial differential equations
-
Barrault M., Maday Y., Nguyen N.C., Patera A.T. An empirical interpolation method: application to efficient reduced-basis discretization of partial differential equations. C.R. Acad. Sci. Paris Ser. 2004, 339:667-672.
-
(2004)
C.R. Acad. Sci. Paris Ser.
, vol.339
, pp. 667-672
-
-
Barrault, M.1
Maday, Y.2
Nguyen, N.C.3
Patera, A.T.4
-
25
-
-
84871659402
-
-
Dimension reduction for unsteady nonlinear partial differential equations via empirical interpolation methods, Master Thesis, Rice University.
-
S. Chaturantabut, Dimension reduction for unsteady nonlinear partial differential equations via empirical interpolation methods, Master Thesis, Rice University, 2008.
-
(2008)
-
-
Chaturantabut, S.1
-
26
-
-
84871661980
-
-
Nonlinear model reduction via discrete empirical interpolation, Ph.D. Thesis, Rice University.
-
S. Chaturantabut, Nonlinear model reduction via discrete empirical interpolation, Ph.D. Thesis, Rice University, 2011.
-
(2011)
-
-
Chaturantabut, S.1
-
27
-
-
79960903533
-
Application of POD and DEIM on dimension reduction of non-linear miscible viscous fingering in porous media
-
Chaturantabut S., Sorensen D.C. Application of POD and DEIM on dimension reduction of non-linear miscible viscous fingering in porous media. Math. Comput. Model. Dynam. Syst. 2011, 17:337-353.
-
(2011)
Math. Comput. Model. Dynam. Syst.
, vol.17
, pp. 337-353
-
-
Chaturantabut, S.1
Sorensen, D.C.2
-
28
-
-
84861371899
-
A state space error estimate for POD-DEIM nonlinear model reduction
-
Chaturantabut S., Sorensen D.C. A state space error estimate for POD-DEIM nonlinear model reduction. SIAM J. Numer. Anal. 2012, 50:46-63.
-
(2012)
SIAM J. Numer. Anal.
, vol.50
, pp. 46-63
-
-
Chaturantabut, S.1
Sorensen, D.C.2
-
29
-
-
38349195074
-
A best points interpolation method for efficient approximation of parametrized functions
-
Nguyen N.C., Patera A.T., Peraire J. A best points interpolation method for efficient approximation of parametrized functions. Int. J. Numer. Methods Engrg. 2008, 73:521-543.
-
(2008)
Int. J. Numer. Methods Engrg.
, vol.73
, pp. 521-543
-
-
Nguyen, N.C.1
Patera, A.T.2
Peraire, J.3
-
30
-
-
53749102512
-
An efficient reduced-order modeling approach for non-linear parametrized partial differential equations
-
Nguyen N.C., Peraire J. An efficient reduced-order modeling approach for non-linear parametrized partial differential equations. Int. J. Numer. Methods Engrg. 2008, 76:27-55.
-
(2008)
Int. J. Numer. Methods Engrg.
, vol.76
, pp. 27-55
-
-
Nguyen, N.C.1
Peraire, J.2
-
31
-
-
34547943108
-
Efficient reduced-basis treatment of nonaffine and nonlinear partial differential equations
-
Grepl M.A., Maday Y., Nguyen N.C., Patera A.T. Efficient reduced-basis treatment of nonaffine and nonlinear partial differential equations. Math. Model. Numer. Anal. 2007, 41:575-605.
-
(2007)
Math. Model. Numer. Anal.
, vol.41
, pp. 575-605
-
-
Grepl, M.A.1
Maday, Y.2
Nguyen, N.C.3
Patera, A.T.4
-
32
-
-
79952654642
-
Efficient non-linear model reduction via a least-squares Petrov-Galerkin projection and compressive tensor approximations
-
Carlberg K., Bou-Mosleh C., Farhat C. Efficient non-linear model reduction via a least-squares Petrov-Galerkin projection and compressive tensor approximations. Int. J. Numer. Methods Engrg. 2011, 86:155-181.
-
(2011)
Int. J. Numer. Methods Engrg.
, vol.86
, pp. 155-181
-
-
Carlberg, K.1
Bou-Mosleh, C.2
Farhat, C.3
-
33
-
-
79959635856
-
State-preserving nonlinear model reduction procedure
-
Chu Y., Serpas M., Hahn J. State-preserving nonlinear model reduction procedure. Chem. Eng. Sci. 2011, 66:3907-3913.
-
(2011)
Chem. Eng. Sci.
, vol.66
, pp. 3907-3913
-
-
Chu, Y.1
Serpas, M.2
Hahn, J.3
-
34
-
-
84870571331
-
Non-linear Petrov-Galerkin methods for reduced order hyperbolic equations and discontinuous finite element methods
-
Fang F., Pain C., Navon I.M., Elsheikh A.H., Du J., Xiao D. Non-linear Petrov-Galerkin methods for reduced order hyperbolic equations and discontinuous finite element methods. J. Comput. Phys. 2013, 234:540-559.
-
(2013)
J. Comput. Phys.
, vol.234
, pp. 540-559
-
-
Fang, F.1
Pain, C.2
Navon, I.M.3
Elsheikh, A.H.4
Du, J.5
Xiao, D.6
-
35
-
-
56949088800
-
A mixed discontinuous/continuous finite element pair for shallow-water ocean modelling
-
Cotter C.J., Ham D.A., Pain C.C. A mixed discontinuous/continuous finite element pair for shallow-water ocean modelling. Ocean Model. 2009, 26:86-90.
-
(2009)
Ocean Model.
, vol.26
, pp. 86-90
-
-
Cotter, C.J.1
Ham, D.A.2
Pain, C.C.3
-
37
-
-
0004540986
-
Tetrahedral mesh optimisation and adaptivity for steady-state and transient finite element calculations
-
Pain C.C., Umpleby A.P., de Oliveira C.R.E., Goddard A.J.H. Tetrahedral mesh optimisation and adaptivity for steady-state and transient finite element calculations. Comput. Methods Appl. Mech. Eng. 2001, 190:3771-3796.
-
(2001)
Comput. Methods Appl. Mech. Eng.
, vol.190
, pp. 3771-3796
-
-
Pain, C.C.1
Umpleby, A.P.2
de Oliveira, C.R.E.3
Goddard, A.J.H.4
-
38
-
-
56549093398
-
LBB stability of a mixed Galerkin finite element pair for fluid flow simulations
-
Cotter C.J., Ham D.A., Pain C.C., Reich S. LBB stability of a mixed Galerkin finite element pair for fluid flow simulations. J. Comput. Phys. 2009, 228:336-348.
-
(2009)
J. Comput. Phys.
, vol.228
, pp. 336-348
-
-
Cotter, C.J.1
Ham, D.A.2
Pain, C.C.3
Reich, S.4
-
39
-
-
84872612270
-
-
POD reduced-order unstructured mesh modeling applied to 2D and 3D fluid flow, Comput. Math. Appl. in press.
-
J. Du, F. Fang, C.C. Pain, I.M. Navon, J. Zhu, D.A. Ham, POD reduced-order unstructured mesh modeling applied to 2D and 3D fluid flow, Comput. Math. Appl. (2012), in press. http://dx.doi.org/10.1016/j.camwa.2012.06.009.
-
(2012)
-
-
Du, J.1
Fang, F.2
Pain, C.C.3
Navon, I.M.4
Zhu, J.5
Ham, D.A.6
-
40
-
-
0022807116
-
A new finite element formulation for computational fluid dynamics: III. The generalized streamline operator for multidimensional advective-diffusive systems
-
Hughes T.J.R., Mallet M. A new finite element formulation for computational fluid dynamics: III. The generalized streamline operator for multidimensional advective-diffusive systems. Comput. Methods Appl. Mech. Engrg. 1986, 58:305-328.
-
(1986)
Comput. Methods Appl. Mech. Engrg.
, vol.58
, pp. 305-328
-
-
Hughes, T.J.R.1
Mallet, M.2
-
41
-
-
0022811673
-
A new finite element formulation for computational fluid dynamics: IV. A discontinuity-capturing operator for multidimensional advective-diffusive systems
-
Hughes T.J.R., Mallet M. A new finite element formulation for computational fluid dynamics: IV. A discontinuity-capturing operator for multidimensional advective-diffusive systems. Comput. Methods Appl. Mech. Engrg. 1986, 58:329-336.
-
(1986)
Comput. Methods Appl. Mech. Engrg.
, vol.58
, pp. 329-336
-
-
Hughes, T.J.R.1
Mallet, M.2
-
42
-
-
0019607241
-
Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations
-
Brooks A.N., Hughes T.J.R. Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations. Comput. Methods Appl. Mech. Engrg. 1982, 32:199-259.
-
(1982)
Comput. Methods Appl. Mech. Engrg.
, vol.32
, pp. 199-259
-
-
Brooks, A.N.1
Hughes, T.J.R.2
-
43
-
-
0027790974
-
A discontinuity-capturing crosswind-dissipation for the finite element solution of the convection-diffusion equation
-
Codina R. A discontinuity-capturing crosswind-dissipation for the finite element solution of the convection-diffusion equation. Comput. Methods Appl. Mech. Engrg. 1993, 110:325-342.
-
(1993)
Comput. Methods Appl. Mech. Engrg.
, vol.110
, pp. 325-342
-
-
Codina, R.1
-
44
-
-
33646481347
-
Space-time streamline upwind Petrov-Galerkin methods for the Boltzmann transport equation
-
Pain C.C., Eaton M.D., Smedley-Stevenson R.P., et al. Space-time streamline upwind Petrov-Galerkin methods for the Boltzmann transport equation. Comput. Methods Appl. Mech. Engrg. 2006, 195:4334-4357.
-
(2006)
Comput. Methods Appl. Mech. Engrg.
, vol.195
, pp. 4334-4357
-
-
Pain, C.C.1
Eaton, M.D.2
Smedley-Stevenson, R.P.3
|