-
1
-
-
77954678113
-
A variance reduction method for parametrized stochastic differential equations using the reduced basis paradigm
-
(Special issue "Mathematical Issues on Complex Fluids" )
-
Boyaval S., Lelièvre T. A variance reduction method for parametrized stochastic differential equations using the reduced basis paradigm. Commun. Math. Sci. 2010, 8:735-762. (Special issue "Mathematical Issues on Complex Fluids" ).
-
(2010)
Commun. Math. Sci.
, vol.8
, pp. 735-762
-
-
Boyaval, S.1
Lelièvre, T.2
-
2
-
-
43049128123
-
A bayesian analysis of the thermal challenge problem
-
(Validation challenge workshop)
-
Liu F., Bayarri M., Berger J., Paulo R., Sacks J. A bayesian analysis of the thermal challenge problem. Comput. Methods Appl. Mech Eng. 2008, 197:2457-2466. (Validation challenge workshop).
-
(2008)
Comput. Methods Appl. Mech Eng.
, vol.197
, pp. 2457-2466
-
-
Liu, F.1
Bayarri, M.2
Berger, J.3
Paulo, R.4
Sacks, J.5
-
5
-
-
16244382554
-
Numerical challenges in the use of polynomial chaos representations for stochastic processes
-
Debusschere B., Najm H., Pebay P., Knio O., Ghanem R., Maître O.L. Numerical challenges in the use of polynomial chaos representations for stochastic processes. SIAM J. Sci. Comput. 2004, 26:698-719.
-
(2004)
SIAM J. Sci. Comput.
, vol.26
, pp. 698-719
-
-
Debusschere, B.1
Najm, H.2
Pebay, P.3
Knio, O.4
Ghanem, R.5
Maître, O.L.6
-
6
-
-
45449090596
-
Reduced order modeling of some nonlinear stochastic partial differential equations
-
Burkardt J., Gunzburger M., Webster C. Reduced order modeling of some nonlinear stochastic partial differential equations. Int. J. Numer. Anal. Model. 2007, 4:368-391.
-
(2007)
Int. J. Numer. Anal. Model.
, vol.4
, pp. 368-391
-
-
Burkardt, J.1
Gunzburger, M.2
Webster, C.3
-
8
-
-
9244244173
-
Using Bayesian statistics in the estimation of heat source in radiation
-
Wang J., Zabaras N. Using Bayesian statistics in the estimation of heat source in radiation. Int. J. Heat Mass Transfer 2005, 48:15-29.
-
(2005)
Int. J. Heat Mass Transfer
, vol.48
, pp. 15-29
-
-
Wang, J.1
Zabaras, N.2
-
9
-
-
59149084494
-
Dimensionality reduction and polynomial chaos acceleration of bayesian inference in inverse problems
-
Marzouk Y.M., Najm H.N. Dimensionality reduction and polynomial chaos acceleration of bayesian inference in inverse problems. J. Comput. Phys. 2009, 228:1862-1902.
-
(2009)
J. Comput. Phys.
, vol.228
, pp. 1862-1902
-
-
Marzouk, Y.M.1
Najm, H.N.2
-
10
-
-
33746495084
-
On the construction and analysis of stochastic models: characterization and propagation of the errors associated with limited data
-
Ghanem R.G., Doostan A. On the construction and analysis of stochastic models: characterization and propagation of the errors associated with limited data. J. Comput. Phys. 2006, 217:63-81.
-
(2006)
J. Comput. Phys.
, vol.217
, pp. 63-81
-
-
Ghanem, R.G.1
Doostan, A.2
-
11
-
-
60949108887
-
Construction of probability distributions in high dimension using the maximum entropy principle: applications to stochastic processes, random fields and random matrices
-
Soize C. Construction of probability distributions in high dimension using the maximum entropy principle: applications to stochastic processes, random fields and random matrices. Int. J. Numer. Methods Eng. 2008, 76:1583-1611.
-
(2008)
Int. J. Numer. Methods Eng.
, vol.76
, pp. 1583-1611
-
-
Soize, C.1
-
12
-
-
77957936449
-
Convergence rates of best N-term Galerkin approximations for a class of elliptic sPDEs
-
Cohen A., DeVore R., Schwab C. Convergence rates of best N-term Galerkin approximations for a class of elliptic sPDEs. Found. Comput. Math. 2010, 10:615-646.
-
(2010)
Found. Comput. Math.
, vol.10
, pp. 615-646
-
-
Cohen, A.1
DeVore, R.2
Schwab, C.3
-
13
-
-
78751652284
-
Analytic regularity and polynomial approximation of parametric stochastic elliptic pdes
-
Cohen A., Devore R., Schwab C. Analytic regularity and polynomial approximation of parametric stochastic elliptic pdes. Anal. Appl. 2011, 9:11-47.
-
(2011)
Anal. Appl.
, vol.9
, pp. 11-47
-
-
Cohen, A.1
Devore, R.2
Schwab, C.3
-
14
-
-
69749114337
-
A reduced basis approach for variational problems with stochastic parameters: Application to heat conduction with variable robin coefficient
-
Boyaval S., Le Bris C., Maday Y., Nguyen N., Patera A. A reduced basis approach for variational problems with stochastic parameters: Application to heat conduction with variable robin coefficient. Comput. Methods Appl. Mech. Eng. 2009, 198:3187-3206.
-
(2009)
Comput. Methods Appl. Mech. Eng.
, vol.198
, pp. 3187-3206
-
-
Boyaval, S.1
Le Bris, C.2
Maday, Y.3
Nguyen, N.4
Patera, A.5
-
15
-
-
84859777710
-
Adaptive reduced basis strategy based on goal oriented error assessment for stochastic problems
-
Florentin E., Díez P. Adaptive reduced basis strategy based on goal oriented error assessment for stochastic problems. Comput. Methods Appl. Mech. Eng. 2012, 225-228:116-127.
-
(2012)
Comput. Methods Appl. Mech. Eng.
, pp. 116-127
-
-
Florentin, E.1
Díez, P.2
-
16
-
-
0002522806
-
When are quasi-Monte Carlo algorithms efficient for high-dimensional integrals?
-
Sloan I.H., Woźniakowski H. When are quasi-Monte Carlo algorithms efficient for high-dimensional integrals?. J. Complexity 1998, 14:1-33.
-
(1998)
J. Complexity
, vol.14
, pp. 1-33
-
-
Sloan, I.H.1
Woźniakowski, H.2
-
17
-
-
12444310208
-
Quasi-monte carlo algorithms for diffusion equations in high dimensions
-
Venkiteswaran G., Junk M. Quasi-monte carlo algorithms for diffusion equations in high dimensions. Math. Comput. Simul. 2005, 68:23-41.
-
(2005)
Math. Comput. Simul.
, vol.68
, pp. 23-41
-
-
Venkiteswaran, G.1
Junk, M.2
-
18
-
-
84861825674
-
Quasi-Monte Carlo finite element methods for a class of elliptic partial differential equations with random coefficients
-
Technical Report 52, ETH SAM Report
-
F. Kuo, C. Schwab, I. Sloan, Quasi-Monte Carlo finite element methods for a class of elliptic partial differential equations with random coefficients, Technical Report 52, ETH SAM Report, 2011.
-
(2011)
-
-
Kuo, F.1
Schwab, C.2
Sloan, I.3
-
20
-
-
84865358644
-
-
B. Jourdain, Advanced financial modelling, Radon Series Comp. Appl. Math, vol. 8, De Gruyter, pp. 205-222.
-
Advanced financial modelling, Radon Series Comp. Appl. Math, De Gruyter
, vol.8
, pp. 205-222
-
-
Jourdain, B.1
-
21
-
-
67349223776
-
Reduced basis approximation and a posteriori error estimation for parametrized parabolic pdes; application to real-time Bayesian parameter estimation
-
in: L. Biegler, G. Biros, O. Ghattas, M. Heinkenschloss, D. Keyes, B. Mallick, Y. Marzouk, L. Tenorio, B. van Bloemen Waanders, K. Willcox (Eds.), Computational Methods for Large Scale Inverse Problems and Uncertainty Quantification, Jhon Wiley & Sons, UK.
-
N.C. Nguyen, G. Rozza, D.B.P. Huynh, A.T. Patera, Reduced basis approximation and a posteriori error estimation for parametrized parabolic pdes; application to real-time Bayesian parameter estimation, in: L. Biegler, G. Biros, O. Ghattas, M. Heinkenschloss, D. Keyes, B. Mallick, Y. Marzouk, L. Tenorio, B. van Bloemen Waanders, K. Willcox (Eds.), Computational Methods for Large Scale Inverse Problems and Uncertainty Quantification, Jhon Wiley & Sons, UK.
-
-
-
Nguyen, N.C.1
Rozza, G.2
Huynh, D.B.P.3
Patera, A.T.4
-
22
-
-
78549269733
-
Reduced basis techniques for stochastic problems
-
(Special issue E. Cueto, F. Chinesta, P. Ladeveze and A. Nouy ed.)
-
Boyaval S., Le Bris C., Lelièvre T., Maday Y., Nguyen N., Patera A.T. Reduced basis techniques for stochastic problems. Archives Comput Methods Eng. 2010, 17:454. (Special issue E. Cueto, F. Chinesta, P. Ladeveze and A. Nouy ed.). 10.1007/s11831-010-9056-z.
-
(2010)
Archives Comput Methods Eng.
, vol.17
, pp. 454
-
-
Boyaval, S.1
Le Bris, C.2
Lelièvre, T.3
Maday, Y.4
Nguyen, N.5
Patera, A.T.6
-
23
-
-
84875826962
-
Reduced-basis method for the rapid and reliable solution of partial differential equations
-
Madrid, European Mathematical Society Eds.
-
Y. Maday, Reduced-basis method for the rapid and reliable solution of partial differential equations, in: Proceedings of International Conference of Mathematicians, Madrid, European Mathematical Society Eds., 2006.
-
(2006)
in: Proceedings of International Conference of Mathematicians
-
-
Maday, Y.1
-
24
-
-
84865358645
-
-
Reduced Basis Approximation and A Posteriori Error Estimation for Parametrized Partial Differential Equations, Copyright MIT, 2006-2007. MIT Pappalardo Monographs in Mechanical Engineering, in preparation.
-
A.T. Patera, G. Rozza, Reduced Basis Approximation and A Posteriori Error Estimation for Parametrized Partial Differential Equations, Copyright MIT, 2006-2007. MIT Pappalardo Monographs in Mechanical Engineering, in preparation.
-
-
-
Patera, A.T.1
Rozza, G.2
-
25
-
-
0037906854
-
A priori convergence theory for reduced-basis approximations of single-parameter elliptic partial differential equations
-
Maday Y., Patera A.T., Turinici G. A priori convergence theory for reduced-basis approximations of single-parameter elliptic partial differential equations. J. Sci. Comput. 2002, 17:437-446.
-
(2002)
J. Sci. Comput.
, vol.17
, pp. 437-446
-
-
Maday, Y.1
Patera, A.T.2
Turinici, G.3
-
26
-
-
0037715324
-
Global a priori convergence theory for reduced-basis approximations of single-parameter symmetric coercive elliptic partial differential equations
-
Maday Y., Patera A., Turinici G. Global a priori convergence theory for reduced-basis approximations of single-parameter symmetric coercive elliptic partial differential equations. C.R. Acad. Sci. Paris Ser. I 2002, 335:289-294.
-
(2002)
C.R. Acad. Sci. Paris Ser. I
, vol.335
, pp. 289-294
-
-
Maday, Y.1
Patera, A.2
Turinici, G.3
-
28
-
-
84855846712
-
A priori convergence of the greedy algorithm for the parametrized reduced basis
-
Buffa A., Maday Y., Patera A.T., Prud'homme C., Turinici G. A priori convergence of the greedy algorithm for the parametrized reduced basis. Math. Model. Numer Anal. 2012, 43:595-603.
-
(2012)
Math. Model. Numer Anal.
, vol.43
, pp. 595-603
-
-
Buffa, A.1
Maday, Y.2
Patera, A.T.3
Prud'homme, C.4
Turinici, G.5
-
29
-
-
79960391988
-
Convergence rates for greedy algorithms in reduced basis methods
-
Binev P., Cohen W., Dahmen Albert, DeVore R., Petrova G., Wojtaszczyk P. Convergence rates for greedy algorithms in reduced basis methods. SIAM J. Math. Anal. 2011, 43:1457-1472.
-
(2011)
SIAM J. Math. Anal.
, vol.43
, pp. 1457-1472
-
-
Binev, P.1
Cohen, W.2
Dahmen, A.3
DeVore, R.4
Petrova, G.5
Wojtaszczyk, P.6
-
30
-
-
0345745619
-
Note on a method for calculating corrected sums of squares and products
-
Welford B.P. Note on a method for calculating corrected sums of squares and products. Technometric 1962, 4:419-420.
-
(1962)
Technometric
, vol.4
, pp. 419-420
-
-
Welford, B.P.1
-
31
-
-
0018518780
-
Updating mean variance estimates: an improved Communications of the ACM method
-
West D. Updating mean variance estimates: an improved Communications of the ACM method. Sci. Appl. 1979, 22:532-535.
-
(1979)
Sci. Appl.
, vol.22
, pp. 532-535
-
-
West, D.1
-
33
-
-
15744376916
-
Certified real-time solution of parametrized partial differential equations
-
Springer, S. Yip (Ed.)
-
Nguyen N.C., Veroy K., Patera A.T. Certified real-time solution of parametrized partial differential equations. Handbook of Materials Modeling 2005, 1523-1558. Springer. S. Yip (Ed.).
-
(2005)
Handbook of Materials Modeling
, pp. 1523-1558
-
-
Nguyen, N.C.1
Veroy, K.2
Patera, A.T.3
-
34
-
-
13844308726
-
Galerkin methods for linear and nonlinear elliptic stochastic pdes
-
Matthies H., Keese A. Galerkin methods for linear and nonlinear elliptic stochastic pdes. Comput. Meth. Appl. Mech. Eng. 2005, 194:1295-1331.
-
(2005)
Comput. Meth. Appl. Mech. Eng.
, vol.194
, pp. 1295-1331
-
-
Matthies, H.1
Keese, A.2
-
35
-
-
34548216854
-
A stochastic collocation method for elliptic partial differential equations with random input data
-
Babuška I., Nobile F., Tempone R. A stochastic collocation method for elliptic partial differential equations with random input data. SIAM J. Numer. Anal. 2007, 45:1005-1034.
-
(2007)
SIAM J. Numer. Anal.
, vol.45
, pp. 1005-1034
-
-
Babuška, I.1
Nobile, F.2
Tempone, R.3
-
36
-
-
10444261986
-
Deterministic FEM for elliptic problems with stochastic coefficients
-
Frauenfelder P., Schwab C., Todor R. Deterministic FEM for elliptic problems with stochastic coefficients. Comput. Math. Appl. Mech. Eng. 2005, 194:205-228.
-
(2005)
Comput. Math. Appl. Mech. Eng.
, vol.194
, pp. 205-228
-
-
Frauenfelder, P.1
Schwab, C.2
Todor, R.3
-
37
-
-
33746346426
-
Karhunen-loève approximation of random fields by generalized fast multipole methods
-
Schwab C., Todor R. Karhunen-loève approximation of random fields by generalized fast multipole methods. J. Comput. Phys. 2006, 217:100-122.
-
(2006)
J. Comput. Phys.
, vol.217
, pp. 100-122
-
-
Schwab, C.1
Todor, R.2
-
38
-
-
34548290926
-
A generalized spectral decomposition technique to solve a class of linear stochastic partial differential equations
-
Nouy A. A generalized spectral decomposition technique to solve a class of linear stochastic partial differential equations. Comput. Methods Appl. Mech. Eng. 2007, 196:4521-4537.
-
(2007)
Comput. Methods Appl. Mech. Eng.
, vol.196
, pp. 4521-4537
-
-
Nouy, A.1
-
39
-
-
33947240401
-
Preconditioning markov chain monte carlo simulations using coarse-scale models
-
Efendiev Y., Hou T., Luo W. Preconditioning markov chain monte carlo simulations using coarse-scale models. SIAM J. Sci. Comput. 2006, 28:776-803.
-
(2006)
SIAM J. Sci. Comput.
, vol.28
, pp. 776-803
-
-
Efendiev, Y.1
Hou, T.2
Luo, W.3
-
40
-
-
0034660787
-
Output bounds for reduced-basis approximations of symmetric positive definite eigenvalue problems
-
Machiels L., Maday Y., Oliveira I.B., Patera A.T., Rovas D. Output bounds for reduced-basis approximations of symmetric positive definite eigenvalue problems. C.R. Acad. Sci. Paris Série I 2000, 331:153-158.
-
(2000)
C.R. Acad. Sci. Paris Série I
, vol.331
, pp. 153-158
-
-
Machiels, L.1
Maday, Y.2
Oliveira, I.B.3
Patera, A.T.4
Rovas, D.5
-
41
-
-
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.T., Turinici G. Reliable real-time solution of parametrized partial differential equations: reduced-basis output bounds methods. J. Fluids Eng. 2002, 124:70-80.
-
(2002)
J. Fluids Eng.
, vol.124
, pp. 70-80
-
-
Prud'homme, C.1
Rovas, D.2
Veroy, K.3
Maday, Y.4
Patera, A.T.5
Turinici, G.6
-
42
-
-
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., Patera A.T. Reduced basis approximation and a posteriori error estimation for affinely parametrized elliptic coercive partial differential equations - application to transport and continuum mechanics. Arch. Comput. Methods Eng. 2008, 15:229-275.
-
(2008)
Arch. Comput. Methods Eng.
, vol.15
, pp. 229-275
-
-
Rozza, G.1
Huynh, D.2
Patera, A.T.3
-
43
-
-
80054960849
-
Multilevel monte carlo methods and applications to elliptic pdes with random coefficients
-
Cliffe R.S.K.A., Giles M.B., Teckentrup A. Multilevel monte carlo methods and applications to elliptic pdes with random coefficients. Comput. Visual. Sci. 2011, 14:3-15.
-
(2011)
Comput. Visual. Sci.
, vol.14
, pp. 3-15
-
-
Cliffe, R.S.K.A.1
Giles, M.B.2
Teckentrup, A.3
-
44
-
-
0242462295
-
The Bayesian choice: from decision-theoretic foundations to computational implementation
-
Springer-Verlag, New York
-
Robert C.P. The Bayesian choice: from decision-theoretic foundations to computational implementation. Springer Texts in Statistics 2007, Springer-Verlag, New York.
-
(2007)
Springer Texts in Statistics
-
-
Robert, C.P.1
-
45
-
-
84865358646
-
-
Statistical inference, The Wadsworth & Brooks/Cole Statistics/Probability Series, Wadsworth & Brooks/Cole Advanced Books & Software, Pacific Grove, CA
-
G. Casella, R.L. Berger, Statistical inference, The Wadsworth & Brooks/Cole Statistics/Probability Series, Wadsworth & Brooks/Cole Advanced Books & Software, Pacific Grove, CA, 1990.
-
(1990)
-
-
Casella, G.1
Berger, R.L.2
|