-
1
-
-
0017970146
-
Automatic choice of global shape functions in structural analysis
-
Almroth, B.O., Stern, P. and Brogan, F.A. 1978 Automatic choice of global shape functions in structural analysis. AIAA Journal 16, 525-528.
-
(1978)
AIAA Journal
, vol.16
, pp. 525-528
-
-
Almroth, B.O.1
Stern, P.2
Brogan, F.A.3
-
2
-
-
47749108243
-
Interpolation method for adapting reduced-order models and application to aeroelasticity
-
Amsallem, D. and Farhat, C. 2008 Interpolation method for adapting reduced-order models and application to aeroelasticity. AIAA Journal 46(7), 1803-1813.
-
(2008)
AIAA Journal
, vol.46
, Issue.7
, pp. 1803-1813
-
-
Amsallem, D.1
Farhat, C.2
-
3
-
-
78549259439
-
On-demand CFD-based aeroelastic predictions using a database of reduced-order bases and models
-
Paper 2009-800
-
Amsallem, D., Cortial, J. and Farhat, C. 2009 On-demand CFD-based aeroelastic predictions using a database of reduced-order bases and models. 47th AIAA Aerospace Sciences Meeting, Including the New Horizons Forum and Aerospace Exposition, 5-8 January 2009, Orlando, Florida. Paper 2009-800.
-
(2009)
47th AIAA Aerospace Sciences Meeting, Including the New Horizons Forum and Aerospace Exposition, 5-8 January 2009, Orlando, Florida
-
-
Amsallem, D.1
Cortial, J.2
Farhat, C.3
-
4
-
-
0030193808
-
Parametric families of reduced finite element models: Theory and applications
-
Balmes, E. 1996 Parametric families of reduced finite element models: Theory and applications. Mechanical Systems and Signal Processing 10(4), 381-394.
-
(1996)
Mechanical Systems and Signal Processing
, vol.10
, Issue.4
, pp. 381-394
-
-
Balmes, E.1
-
5
-
-
15744385841
-
An ‘empirical interpolation’ method: Application to efficient reduced-basis discretization of partial differential equations
-
Barrault, M., Maday, Y., Nguyen, N.C. and Patera, A.T. 2004 An ‘empirical interpolation’ method: Application to efficient reduced-basis discretization of partial differential equations. C. R. Acad. Sci. Paris, Série I. 339, 667-672.
-
(2004)
C. R. Acad. Sci. Paris, Série I
, vol.339
, pp. 667-672
-
-
Barrault, M.1
Maday, Y.2
Nguyen, N.C.3
Patera, A.T.4
-
6
-
-
53349166973
-
Reduced-basis approach for homogenization beyond the periodic setting
-
Boyaval, S. 2008 Reduced-basis approach for homogenization beyond the periodic setting. SIAM Multiscale Modeling & Simulation 7(1), 466-494.
-
(2008)
SIAM Multiscale Modeling & Simulation
, vol.7
, Issue.1
, pp. 466-494
-
-
Boyaval, S.1
-
7
-
-
84885535773
-
A reduced-basis approach for variational problems with stochastic parameters: Application to heat conduction with variable robin coefficient
-
Boyaval, S., Le Bris, C., Nguyen, N.C. and Patera, A.T. 2008 A reduced-basis approach for variational problems with stochastic parameters: Application to heat conduction with variable robin coefficient. Comp. Meth. Appl. Mech. and Eng.
-
(2008)
Comp. Meth. Appl. Mech. and Eng
-
-
Boyaval, S.1
Le Bris, C.2
Nguyen, N.C.3
Patera, A.T.4
-
9
-
-
39049136105
-
Feasibility and competitiveness of a reduced basis approach for rapid electronic structure calculations in quantum chemistry
-
Cances, E., Le Bris, C., Nguyen, N.C., Maday, Y., Patera, A.T. and Pau, G.S.H. 2007 Feasibility and competitiveness of a reduced basis approach for rapid electronic structure calculations in quantum chemistry. Proceedings of the Workshop for High-dimensional Partial Differential Equations in Science and Engineering (Montreal).
-
(2007)
Proceedings of the Workshop for High-dimensional Partial Differential Equations in Science and Engineering (Montreal)
-
-
Cances, E.1
Le Bris, C.2
Nguyen, N.C.3
Maday, Y.4
Patera, A.T.5
Pau, G.S.H.6
-
10
-
-
0033295675
-
Evaluation of pod-based decomposition techniques applied to parameter-dependent non-turbulent flows
-
Christensen, E.A., Brons, M. and Sorensen, J.N. 2000 Evaluation of pod-based decomposition techniques applied to parameter-dependent non-turbulent flows. SIAM J. Sci. Comput. 21, 1419-1434.
-
(2000)
SIAM J. Sci. Comput
, vol.21
, pp. 1419-1434
-
-
Christensen, E.A.1
Brons, M.2
Sorensen, J.N.3
-
11
-
-
0003545358
-
-
Chicago Lectures in Mathematics. University of Chicago Press, Chicago, IL
-
Constantin, P. and Foias, C. 1988 Navier-Stokes Equations. Chicago Lectures in Mathematics. University of Chicago Press, Chicago, IL.
-
(1988)
Navier-Stokes Equations
-
-
Constantin, P.1
Foias, C.2
-
12
-
-
0026067446
-
Low-dimensional models for complex geometry flows: Application to grooved channels and circular cylinders
-
Deane, A., Kevrekidis, I., Karniadakis, G. and Orszag, S. 1991 Low-dimensional models for complex geometry flows: Application to grooved channels and circular cylinders. Phys. Fluids 10, 2337-2354.
-
(1991)
Phys. Fluids
, vol.10
, pp. 2337-2354
-
-
Deane, A.1
Kevrekidis, I.2
Karniadakis, G.3
Orszag, S.4
-
13
-
-
55349102713
-
Reduced basis error bound computation of parameter-dependent Navier-Stokes equations by the natural norm approach
-
Deparis, S. 2008 Reduced basis error bound computation of parameter-dependent Navier-Stokes equations by the natural norm approach. SIAM Journal of Numerical Analysis 46, 2039-2067.
-
(2008)
SIAM Journal of Numerical Analysis
, vol.46
, pp. 2039-2067
-
-
Deparis, S.1
-
14
-
-
0020547404
-
On the error behavior of the reduced basis technique for nonlinear finite element approximations
-
Fink, J.P. and Rheinboldt, W.C. 1983 On the error behavior of the reduced basis technique for nonlinear finite element approximations. Z. Angew. Math. Mech. 63(1), 21-28.
-
(1983)
Z. Angew. Math. Mech
, vol.63
, Issue.1
, pp. 21-28
-
-
Fink, J.P.1
Rheinboldt, W.C.2
-
16
-
-
15744385753
-
A posteriori error bounds for reduced-basis approximations of parametrized parabolic partial differential equations
-
Grepl, M.A. and Patera, A.T. 2005 A posteriori error bounds for reduced-basis approximations of parametrized parabolic partial differential equations. M2AN (Math. Model. Numer. Anal.) 39(1), 157-181.
-
(2005)
M2AN (Math. Model. Numer. Anal.)
, vol.39
, Issue.1
, pp. 157-181
-
-
Grepl, M.A.1
Patera, A.T.2
-
17
-
-
34547943108
-
Efficient reducedbasis treatment of nonaffine and nonlinear partial differential equations
-
Grepl, M.A., Maday, Y., Nguyen, N.C. and Patera, A.T. 2007a Efficient reducedbasis treatment of nonaffine and nonlinear partial differential equations. M2AN (Math. Model. Numer. Anal.) 41, 575-605.
-
(2007)
M2AN (Math. Model. Numer. Anal.)
, vol.41
, pp. 575-605
-
-
Grepl, M.A.1
Maday, Y.2
Nguyen, N.C.3
Patera, A.T.4
-
18
-
-
55349141348
-
Certified rapid solution of partial differential equations for real-time parameter estimation and optimization
-
(ed. Biegler, L.T., Ghattas, O., Heinkenschloss, M., Keyes, D. and van B. Wandeers, B.), SIAM Computational Science and Engineering Book Series
-
Grepl, M.A., Nguyen, N.C., Veroy, K., Patera, A.T. and Liu, G.R. 2007b Certified rapid solution of partial differential equations for real-time parameter estimation and optimization. In Proceedings of the 2 nd Sandia Workshop of PDE-Constrained Optimization: Real-Time PDE-Constrained Optimization (ed. Biegler, L.T., Ghattas, O., Heinkenschloss, M., Keyes, D. and van B. Wandeers, B.), pp. 197-216 SIAM Computational Science and Engineering Book Series.
-
(2007)
Proceedings of the 2 nd Sandia Workshop of PDE-Constrained Optimization: Real-Time PDE-Constrained Optimization
, pp. 197-216
-
-
Grepl, M.A.1
Nguyen, N.C.2
Veroy, K.3
Patera, A.T.4
Liu, G.R.5
-
20
-
-
33750482967
-
Reduced-order modeling of time-dependent PDEs with multiple parameters in the boundary data
-
Gunzburger, M.D., Peterson, J. and Shadid, J.N. 2007 Reduced-order modeling of time-dependent PDEs with multiple parameters in the boundary data. Comp. Meth. Applied Mech. 196, 1030-1047.
-
(2007)
Comp. Meth. Applied Mech
, vol.196
, pp. 1030-1047
-
-
Gunzburger, M.D.1
Peterson, J.2
Shadid, J.N.3
-
21
-
-
41549118036
-
Reduced basis method for finite volume approximations of parametrized evolution equations
-
Haasdonk, B. and Ohlberger, M. 2008 Reduced basis method for finite volume approximations of parametrized evolution equations. M2AN (Math. Model. Numer. Anal.) 42(2), 277-302.
-
(2008)
M2AN (Math. Model. Numer. Anal.)
, vol.42
, Issue.2
, pp. 277-302
-
-
Haasdonk, B.1
Ohlberger, M.2
-
22
-
-
33750977082
-
Proper orthogonal decomposition surrogate models for nonlinear dynamical systems: Error estimates and suboptimal control
-
Springer
-
Hinze, M. and Volkwein, S. 2005 Proper orthogonal decomposition surrogate models for nonlinear dynamical systems: error estimates and suboptimal control. Lecture Notes in Computational Science and Engineering vol. 45 Springer.
-
(2005)
Lecture Notes in Computational Science and Engineering
, vol.45
-
-
Hinze, M.1
Volkwein, S.2
-
23
-
-
84874354330
-
-
Copyright MIT, Technology Licensing Office, case 12600, Cambridge, MA
-
Huynh, D.B.P., Nguyen, N.C., Rozza, G. and Patera, A.T. 2007-2009 rbMIT Software:http://augustine.mit.edu/methodology/methodology rbMIT System.htm. Copyright MIT, Technology Licensing Office, case 12600, Cambridge, MA.
-
(2007)
rbMIT Software:
-
-
Huynh, D.B.P.1
Nguyen, N.C.2
Rozza, G.3
Patera, A.T.4
-
24
-
-
36148955493
-
A successive constraint linear optimization method for lower bounds of parametric coercivity and inf-sup stability constants
-
Huynh, D.B.P., Rozza, G., Sen, S. and Patera, A.T. 2007 A successive constraint linear optimization method for lower bounds of parametric coercivity and inf-sup stability constants. C. R. Acad. Sci. Paris, Analyse Numérique 345(8), 473-478.
-
(2007)
C. R. Acad. Sci. Paris, Analyse Numérique
, vol.345
, Issue.8
, pp. 473-478
-
-
Huynh, D.B.P.1
Rozza, G.2
Sen, S.3
Patera, A.T.4
-
25
-
-
0004159331
-
A reduced basis method for control problems governed by PDEs
-
(ed. Desch, W., Kappel, F. and Kunisch, K.) Birkhauser
-
Ito, K. and Ravindran, S.S. 1998a A reduced basis method for control problems governed by PDEs. In Control and Estimation of Distributed Parameter Systems (ed. Desch, W., Kappel, F. and Kunisch, K.) Birkhauser pp. 153-168.
-
(1998)
Control and Estimation of Distributed Parameter Systems
, pp. 153-168
-
-
Ito, K.1
Ravindran, S.S.2
-
26
-
-
0000104411
-
A reduced-order method for simulation and control of fluid flows
-
Ito, K. and Ravindran, S.S. 1998b A reduced-order method for simulation and control of fluid flows. Journal of Computational Physics 143(2), 403-425.
-
(1998)
Journal of Computational Physics
, vol.143
, Issue.2
, pp. 403-425
-
-
Ito, K.1
Ravindran, S.S.2
-
28
-
-
26844562908
-
Reduced-basis modeling of turbulent plane channel flow
-
Johansson, P.S., Andersson, H. and Rønquist, E. 2006 Reduced-basis modeling of turbulent plane channel flow. Computers and Fluids 35(2), 189-207.
-
(2006)
Computers and Fluids
, vol.35
, Issue.2
, pp. 189-207
-
-
Johansson, P.S.1
Andersson, H.2
Rønquist, E.3
-
29
-
-
0001255117
-
Numerical and hydrodynamic stability: Towards error control in computational fluid dynamics
-
Johnson, C., Rannacher, R. and Boman, M. 1995 Numerical and hydrodynamic stability: Towards error control in computational fluid dynamics. SIAM Journal of Numerical Analysis 32(4), 1058-1079.
-
(1995)
SIAM Journal of Numerical Analysis
, vol.32
, Issue.4
, pp. 1058-1079
-
-
Johnson, C.1
Rannacher, R.2
Boman, M.3
-
30
-
-
0003353850
-
Stability of fluid motions. I. & II
-
& 28 of, Springer-Verlag, New York
-
Joseph, D. 1976 Stability of fluid motions. I. & II. vol. 27 & 28 of Springer Tracts in Natural Philosophy. Springer-Verlag, New York.
-
(1976)
Springer Tracts in Natural Philosophy
, vol.27
-
-
Joseph, D.1
-
31
-
-
84974274856
-
Minimum-dissipation transport enhancement by flow destabilization - Reynolds’ analogy revisited
-
Karniadakis, G.E., Mikic, B.B. and Patera, A.T. 1988 Minimum-dissipation transport enhancement by flow destabilization - Reynolds’ analogy revisited. Journal of Fluid Mechanics 192, 365-391.
-
(1988)
Journal of Fluid Mechanics
, vol.192
, pp. 365-391
-
-
Karniadakis, G.E.1
Mikic, B.B.2
Patera, A.T.3
-
32
-
-
77950795079
-
A certified reduced basis method for fokker-planck equation of dilute polymeric fluids: Fene dumbbells in extensional flow
-
Submitted
-
Knezevic, D. and Patera, A.T. 2009 A certified reduced basis method for fokker-planck equation of dilute polymeric fluids: Fene dumbbells in extensional flow. SIAM J. Sci. Comput. Submitted.
-
(2009)
SIAM J. Sci. Comput
-
-
Knezevic, D.1
Patera, A.T.2
-
33
-
-
0038693394
-
Galerkin proper orthogonal decomposition methods for a general equation in fluid dynamics
-
Kunisch, K. and Volkwein, S. 2002 Galerkin proper orthogonal decomposition methods for a general equation in fluid dynamics. SIAM J. Num. Analysis 40(2), 492-515.
-
(2002)
SIAM J. Num. Analysis
, vol.40
, Issue.2
, pp. 492-515
-
-
Kunisch, K.1
Volkwein, S.2
-
34
-
-
0033177060
-
Control of Burgers’ equation by a reduced order approach using proper orthogonal decomposition
-
Kunish, K. and Volkwein, S. 1999 Control of Burgers’ equation by a reduced order approach using proper orthogonal decomposition. J. Optimization Theory and Applications 102, 345-371.
-
(1999)
J. Optimization Theory and Applications
, vol.102
, pp. 345-371
-
-
Kunish, K.1
Volkwein, S.2
-
35
-
-
0037906854
-
A Priori convergence theory for reduced-basis approximations of single-parameter elliptic partial differential equations
-
Maday, Y., Patera, A. and Turinici, G. 2002 A Priori convergence theory for reduced-basis approximations of single-parameter elliptic partial differential equations. Journal of Scientific Computing 17(1-4), 437-446.
-
(2002)
Journal of Scientific Computing
, vol.17
, Issue.1-4
, pp. 437-446
-
-
Maday, Y.1
Patera, A.2
Turinici, G.3
-
37
-
-
84885535181
-
Efficient and robust parameter estimation using the reduced basis method: Application to the inverse scattering problem
-
Nguyen, N.C. 2008 Efficient and robust parameter estimation using the reduced basis method: Application to the inverse scattering problem. SIAM J. Sci. Comput.
-
(2008)
SIAM J. Sci. Comput
-
-
Nguyen, N.C.1
-
38
-
-
53349103005
-
A multiscale reduced-basis method for parametrized elliptic partial differential equations with multiple scales
-
Nguyen, N.C. 2008 A multiscale reduced-basis method for parametrized elliptic partial differential equations with multiple scales. Journal of Computational Physics 227(23), 9807-9822.
-
(2008)
Journal of Computational Physics
, vol.227
, Issue.23
, pp. 9807-9822
-
-
Nguyen, N.C.1
-
39
-
-
70349560243
-
Reduced basis approximation and a posteriori error estimation for the time-dependent viscous burgers equation
-
Nguyen, N.C., Rozza, G. and Patera, A.T. 2009 Reduced basis approximation and a posteriori error estimation for the time-dependent viscous burgers equation. Calcolo 46, 157-185.
-
(2009)
Calcolo
, vol.46
, pp. 157-185
-
-
Nguyen, N.C.1
Rozza, G.2
Patera, A.T.3
-
40
-
-
8644264522
-
Certified real-time solution of parametrized partial differential equations
-
(ed. Yip, S.) Springer
-
Nguyen, N.C., Veroy, K. and Patera, A.T. 2005 Certified real-time solution of parametrized partial differential equations. In Handbook of Materials Modeling (ed. Yip, S.) Springer pp. 1523-1558.
-
(2005)
Handbook of Materials Modeling
, pp. 1523-1558
-
-
Nguyen, N.C.1
Veroy, K.2
Patera, A.T.3
-
41
-
-
0019009732
-
Reduced basis technique for nonlinear analysis of structures
-
Noor, A.K. and Peters, J.M. 1980 Reduced basis technique for nonlinear analysis of structures. AIAA Journal 18(4), 455-462.
-
(1980)
AIAA Journal
, vol.18
, Issue.4
, pp. 455-462
-
-
Noor, A.K.1
Peters, J.M.2
-
42
-
-
0034206154
-
Adjoint recovery of superconvergent functionals from PDE approximations
-
Pierce, N. and Giles, M.B. 2000 Adjoint recovery of superconvergent functionals from PDE approximations. SIAM Review 42(2), 247-264.
-
(2000)
SIAM Review
, vol.42
, Issue.2
, pp. 247-264
-
-
Pierce, N.1
Giles, M.B.2
-
43
-
-
84966262223
-
Estimation of the error in the reduced basis method solution of nonlinear equations
-
Porsching, T.A. 1985 Estimation of the error in the reduced basis method solution of nonlinear equations. Mathematics of Computation 45(172), 487-496.
-
(1985)
Mathematics of Computation
, vol.45
, Issue.172
, pp. 487-496
-
-
Porsching, T.A.1
-
44
-
-
0003321083
-
Reliable real-time solution of parametrized partial differential equations:Reduced-basis output bounds methods
-
Prud’homme, C., Rovas, D., Veroy, K., Maday, Y., Patera, A. and Turinici, G. 2002 Reliable real-time solution of parametrized partial differential equations:Reduced-basis output bounds methods. Journal of Fluids Engineering 124(1), 70-80.
-
(2002)
Journal of Fluids Engineering
, vol.124
, Issue.1
, pp. 70-80
-
-
Prud’homme, C.1
Rovas, D.2
Veroy, K.3
Maday, Y.4
Patera, A.5
Turinici, G.6
-
46
-
-
53749107686
-
Reduced basis approximation and a posteriori error estimation for affinely parametrized elliptic coercive partial differential equations: Application to transport and continuum mechanics
-
Rozza, G., Huynh, D.B.P. and Patera, A.T. 2008 Reduced basis approximation and a posteriori error estimation for affinely parametrized elliptic coercive partial differential equations: Application to transport and continuum mechanics. Archives Computational Methods in Engineering 15(3), 229-275.
-
(2008)
Archives Computational Methods in Engineering
, vol.15
, Issue.3
, pp. 229-275
-
-
Rozza, G.1
Huynh, D.B.P.2
Patera, A.T.3
-
47
-
-
33746374294
-
Natural norm’ a posteriori error estimators for reduced basis approximations
-
Sen, S., Veroy, K., Huynh, D.B.P., Deparis, S., Nguyen, N.C. and Patera, A.T. 2006 ‘Natural norm’ a posteriori error estimators for reduced basis approximations. Journal of Computational Physics 217, 37-62.
-
(2006)
Journal of Computational Physics
, vol.217
, pp. 37-62
-
-
Sen, S.1
Veroy, K.2
Huynh, D.B.P.3
Deparis, S.4
Nguyen, N.C.5
Patera, A.T.6
-
49
-
-
15744406041
-
Certified real-time solution of the parametrized steady incompressible Navier-Stokes equations; Rigorous reduced-basis a posteriori error bounds
-
Veroy, K. and Patera, A.T. 2005 Certified real-time solution of the parametrized steady incompressible Navier-Stokes equations; Rigorous reduced-basis a posteriori error bounds. International Journal for Numerical Methods in Fluids 47, 773-788.
-
(2005)
International Journal for Numerical Methods in Fluids
, vol.47
, pp. 773-788
-
-
Veroy, K.1
Patera, A.T.2
-
50
-
-
0345017124
-
Reduced-basis approximation of the viscous Burgers equation: Rigorous a posteriori error bounds
-
Veroy, K., Prud’homme, C. and Patera, A.T. 2003a Reduced-basis approximation of the viscous Burgers equation: Rigorous a posteriori error bounds. C. R. Acad. Sci. Paris, Série I 337(9), 619-624.
-
(2003)
C. R. Acad. Sci. Paris, Série I
, vol.337
, Issue.9
, pp. 619-624
-
-
Veroy, K.1
Prud’homme, C.2
Patera, A.T.3
-
51
-
-
85088184409
-
A Posteriori error bounds for reduced-basis approximation of parametrized noncoercive and nonlinear elliptic partial differential equations
-
Veroy, K., Prud’homme, C., Rovas, D.V. and Patera, A.T. 2003b A Posteriori error bounds for reduced-basis approximation of parametrized noncoercive and nonlinear elliptic partial differential equations. Proceedings of the 16th AIAA Computational Fluid Dynamics Conference. Paper 2003-3847.
-
(2003)
Proceedings of the 16th AIAA Computational Fluid Dynamics Conference
, pp. 2003-3847
-
-
Veroy, K.1
Prud’homme, C.2
Rovas, D.V.3
Patera, A.T.4
-
52
-
-
9244244173
-
Using Bayesian statistics in the estimation of heat source in radiation
-
Wang, J. and Zabaras, N. 2005 Using Bayesian statistics in the estimation of heat source in radiation. International Journal of Heat and Mass Transfer 48, 15-29.
-
(2005)
International Journal of Heat and Mass Transfer
, vol.48
, pp. 15-29
-
-
Wang, J.1
Zabaras, N.2
|