-
1
-
-
0031536737
-
Preconditioning in H(div) and applications
-
D. N. Arnold, R. S. Falk, and R. Winther, Preconditioning in H(div) and applications, Math. Comp., 66 (1997), pp. 957-984.
-
(1997)
Math. Comp.
, vol.66
, pp. 957-984
-
-
Arnold, D.N.1
Falk, R.S.2
Winther, R.3
-
2
-
-
0034386185
-
Multigrid in H(div) and H(curl)
-
D. N. Arnold, R. S. Falk, and R. Winther, Multigrid in H(div) and H(curl), Numer. Math., 85 (2000), pp. 197-217.
-
(2000)
Numer. Math.
, vol.85
, pp. 197-217
-
-
Arnold, D.N.1
Falk, R.S.2
Winther, R.3
-
3
-
-
34548216854
-
A stochastic collocation method for elliptic partial differential equations with random input data
-
I. Babuŝka, F. Nobile, and R. Tempone, A stochastic collocation method for elliptic partial differential equations with random input data, SIAM J. Numer. Anal., 45 (2007), pp. 1005-1034.
-
(2007)
SIAM J. Numer. Anal.
, vol.45
, pp. 1005-1034
-
-
Babuŝka, I.1
Nobile, F.2
Tempone, R.3
-
4
-
-
13844319204
-
Galerkin finite element approximations of stochastic elliptic partial differential equations
-
I. Babuŝka, R. Tempone, and G. E. Zouraris, Galerkin finite element approximations of stochastic elliptic partial differential equations, SIAM J. Numer. Anal., 42 (2004), pp. 800-825.
-
(2004)
SIAM J. Numer. Anal.
, vol.42
, pp. 800-825
-
-
Babuŝka, I.1
Tempone, R.2
Zouraris, G.E.3
-
5
-
-
13844314882
-
Solving elliptic boundary value problems with uncertain coefficients by the finite element method: The stochastic formulation
-
I. Babuŝka, R. Tempone, and G. E. Zouraris, Solving elliptic boundary value problems with uncertain coefficients by the finite element method: The stochastic formulation, Comput. Methods Appl. Mech. Engrg., 194 (2005), pp. 1251-1294.
-
(2005)
Comput. Methods Appl. Mech. Engrg.
, vol.194
, pp. 1251-1294
-
-
Babuŝka, I.1
Tempone, R.2
Zouraris, G.E.3
-
6
-
-
20044390432
-
Numerical solution of saddle point problems
-
M. Benzi, G. H. Golub, and J. Liesen, Numerical solution of saddle point problems, Acta Numer., 14 (2005), pp. 1-137.
-
(2005)
Acta Numer.
, vol.14
, pp. 1-137
-
-
Benzi, M.1
Golub, G.H.2
Liesen, J.3
-
7
-
-
67649493093
-
-
Technical report RAL-TR- 2007-021, SFTC Rutherford Appleton Laboratory, Didcot, UK
-
J. Boyle, M. D. Mihajlović, and J. A. Scott, HSL MI20: An Efficient AMG Preconditioner, Technical report RAL-TR-2007-021, SFTC Rutherford Appleton Laboratory, Didcot, UK, 2007.
-
(2007)
HSL MI20: An Efficient AMG Preconditioner
-
-
Boyle, J.1
Mihajlović, M.D.2
Scott, J.A.3
-
9
-
-
0035964634
-
Solution of stochastic partial differential equations using Galerkin finite element techniques
-
M. K. Deb, I. M. Babuŝka, and J. T. Oden, Solution of stochastic partial differential equations using Galerkin finite element techniques, Comput. Methods Appl. Mech. Engrg., 190 (2001), pp. 6359-6372.
-
(2001)
Comput. Methods Appl. Mech. Engrg.
, vol.190
, pp. 6359-6372
-
-
Deb, M.K.1
Babuŝka, I.M.2
Oden, J.T.3
-
11
-
-
67649534729
-
Efficient solvers for a linear stochastic Galerkin mixed formulation of diffusion problems with random data
-
O. G. Ernst, C. E. Powell, D. J. Silvester, and E. Ullmann, Efficient solvers for a linear stochastic Galerkin mixed formulation of diffusion problems with random data, SIAM J. Sci. Comput., 31 (2009), pp. 1424-1447.
-
(2009)
SIAM J. Sci. Comput.
, vol.31
, pp. 1424-1447
-
-
Ernst, O.G.1
Powell, C.E.2
Silvester, D.J.3
Ullmann, E.4
-
13
-
-
10444261986
-
Finite elements for elliptic problems with stochastic coefficients
-
P. Frauenfelder, C. Schwab, and R. A. Todor, Finite elements for elliptic problems with stochastic coefficients, Comput. Methods Appl. Mech. Engrg., 194 (2005), pp. 205-228.
-
(2005)
Comput. Methods Appl. Mech. Engrg.
, vol.194
, pp. 205-228
-
-
Frauenfelder, P.1
Schwab, C.2
Todor, R.A.3
-
14
-
-
0016562894
-
A stochastic-conceptual analysis of one-dimensional groundwater flow in nonuniform homogeneous media
-
A. Freeze, A stochastic-conceptual analysis of one-dimensional groundwater flow in nonuniform homogeneous media, Water Resour. Res., 11 (1975), pp. 725-740.
-
(1975)
Water Resour. Res.
, vol.11
, pp. 725-740
-
-
Freeze, A.1
-
15
-
-
77956054384
-
H(div) preconditioning for a mixed finite element formulation of the stochastic diffusion problem
-
D. G. Furnival, H. C. Elman, and C. E. Powell, H(div) preconditioning for a mixed finite element formulation of the stochastic diffusion problem, Math. Comp., 79 (2009), pp. 733-760.
-
(2009)
Math. Comp.
, vol.79
, pp. 733-760
-
-
Furnival, D.G.1
Elman, H.C.2
Powell, C.E.3
-
16
-
-
0003241196
-
Iterative methods for solving linear systems
-
SIAM, Philadelphia
-
A. Greenbaum, Iterative Methods for Solving Linear Systems, Frontiers Appl. Math. 17, SIAM, Philadelphia, 1997.
-
(1997)
Frontiers Appl. Math.
, vol.17
-
-
Greenbaum, A.1
-
17
-
-
34247492932
-
Preconditioners for the discretized time-harmonic Maxwell equations in mixed form
-
C. Greif and D. Schötzau, Preconditioners for the discretized time-harmonic Maxwell equations in mixed form, Numer. Linear Algebra Appl., 14 (2007), pp. 281-297.
-
(2007)
Numer. Linear Algebra Appl.
, vol.14
, pp. 281-297
-
-
Greif, C.1
Schötzau, D.2
-
18
-
-
0001252958
-
Multigrid method for H(div) in three dimensions
-
R. Hiptmair, Multigrid method for H(div) in three dimensions, Electron. Trans. Numer. Anal., 6 (1997), pp. 133-152.
-
(1997)
Electron. Trans. Numer. Anal.
, vol.6
, pp. 133-152
-
-
Hiptmair, R.1
-
19
-
-
3042799318
-
An inequality for Hermite polynomials
-
J. Indritz, An inequality for Hermite polynomials, Proc. Amer. Math. Soc., 12 (1961), pp. 981-983.
-
(1961)
Proc. Amer. Math. Soc.
, vol.12
, pp. 981-983
-
-
Indritz, J.1
-
20
-
-
0003876050
-
-
Cambridge University Press Cambridge
-
S. Janson, Gaussian Hilbert Spaces, Cambridge University Press, Cambridge, 1997.
-
(1997)
Gaussian Hilbert Spaces
-
-
Janson, S.1
-
21
-
-
0010600126
-
Nonnegative quadratic forms and bounds on orthogonal polynomials
-
I. Krasikov, Nonnegative quadratic forms and bounds on orthogonal polynomials, J. Approx. Theory, 111 (2001), pp. 31-49.
-
(2001)
J. Approx. Theory
, vol.111
, pp. 31-49
-
-
Krasikov, I.1
-
22
-
-
0003981320
-
-
4th ed., Springer-Verlag, New York
-
M. Loève, Probability Theory, Vol. II, 4th ed., Springer-Verlag, New York, 1978.
-
(1978)
Probability Theory
, vol.2
-
-
Loève, M.1
-
24
-
-
13844308726
-
Galerkin methods for linear and nonlinear elliptic stochastic partial differential equations
-
H. G. Matthies and A. Keese, Galerkin methods for linear and nonlinear elliptic stochastic partial differential equations, Comput. Methods Appl. Mech. Engrg., 194 (2005), pp. 1295-1331.
-
(2005)
Comput. Methods Appl. Mech. Engrg.
, vol.194
, pp. 1295-1331
-
-
Matthies, H.G.1
Keese, A.2
-
25
-
-
0034497397
-
A note on preconditioning for indefinite linear systems
-
M. F. Murphy, G. H. Golub, and A. J. Wathen, A note on preconditioning for indefinite linear systems, SIAM J. Sci. Comput., 21 (2000), pp. 1969-1972.
-
(2000)
SIAM J. Sci. Comput.
, vol.21
, pp. 1969-1972
-
-
Murphy, M.F.1
Golub, G.H.2
Wathen, A.J.3
-
26
-
-
0016555955
-
Solution of sparse indefinite systems of linear equations
-
C. C. Paige and M. A. Saunders, Solution of sparse indefinite systems of linear equations, SIAM J. Numer. Anal., 12 (1975), pp. 617-629.
-
(1975)
SIAM J. Numer. Anal.
, vol.12
, pp. 617-629
-
-
Paige, C.C.1
Saunders, M.A.2
-
27
-
-
0034368563
-
Block-diagonal and indefinite symmetric preconditioners for mixed finite element formulations
-
I. Perugia and V. Simoncini, Block-diagonal and indefinite symmetric preconditioners for mixed finite element formulations, Numer. Linear Algebra Appl., 7 (2000), pp. 585-616.
-
(2000)
Numer. Linear Algebra Appl.
, vol.7
, pp. 585-616
-
-
Perugia, I.1
Simoncini, V.2
-
28
-
-
65249182525
-
Block-diagonal preconditioning for spectral stochastic finite-element systems
-
C. E. Powell and H. C. Elman, Block-diagonal preconditioning for spectral stochastic finite-element systems, IMA J. Numer. Anal., 29 (2009), pp. 350-375.
-
(2009)
IMA J. Numer. Anal.
, vol.29
, pp. 350-375
-
-
Powell, C.E.1
Elman, H.C.2
-
29
-
-
3142782149
-
Optimal preconditioning for Raviart-Thomas mixed formulation of second-order elliptic problems
-
C. E. Powell and D. Silvester, Optimal preconditioning for Raviart-Thomas mixed formulation of second-order elliptic problems, SIAM J. Matrix Anal. Appl., 25 (2003), pp. 718-738.
-
(2003)
SIAM J. Matrix Anal. Appl.
, vol.25
, pp. 718-738
-
-
Powell, C.E.1
Silvester, D.2
-
30
-
-
0001175293
-
A mixed finite element method for second order elliptic problems
-
Springer-Verlag, New York
-
P.-A. Raviart and J. M. Thomas, A mixed finite element method for second order elliptic problems, in Mathematical Aspects of the Finite Element Method, Lecture Notes in Math. 606, Springer-Verlag, New York, 1977, pp. 292-315.
-
(1977)
Mathematical Aspects of the Finite Element Method Lecture Notes in Math
, vol.606
, pp. 292-315
-
-
Raviart, P.-A.1
Thomas, J.M.2
-
31
-
-
77249146405
-
Iterative solvers for the stochastic finite element method
-
E. Rosseel and S. Vandewalle, Iterative solvers for the stochastic finite element method, SIAM J. Sci. Comput., 32 (2010), pp. 372-397.
-
(2010)
SIAM J. Sci. Comput.
, vol.32
, pp. 372-397
-
-
Rosseel, E.1
Vandewalle, S.2
-
32
-
-
33746346426
-
Karhunen-Loève approximation of random fields by generalized fast multipole methods
-
C. Schwab and R. A. Todor, Karhunen-Loève approximation of random fields by generalized fast multipole methods, J. Comput. Phys., 127 (2006), pp. 100-122.
-
(2006)
J. Comput. Phys.
, vol.127
, pp. 100-122
-
-
Schwab, C.1
Todor, R.A.2
-
33
-
-
77950848558
-
A Kronecker product preconditioner for stochastic Galerkin finite element discretizations
-
E. Ullmann, A Kronecker product preconditioner for stochastic Galerkin finite element discretizations, SIAM J. Sci. Comput., 32 (2010), pp. 923-946.
-
(2010)
SIAM J. Sci. Comput.
, vol.32
, pp. 923-946
-
-
Ullmann, E.1
-
34
-
-
0041962347
-
Approximation with Kronecker products, in Linear Algebra for Large Scale and Real-Time Applications
-
Leuven, Belgium, Kluwer Academic Publishers, Dordrecht
-
C. F. Van Loan and N. Pitsianis, Approximation with Kronecker products, in Linear Algebra for Large Scale and Real-Time Applications, in Proceedings of the NATO Advanced Study Institute, Leuven, Belgium, Kluwer Academic Publishers, Dordrecht, 1993, pp. 293-314.
-
(1993)
Proceedings of the NATO Advanced Study Institute
, pp. 293-314
-
-
Van Loan, C.F.1
Pitsianis, N.2
-
35
-
-
21844481759
-
Preconditioning mixed finite element saddle-point elliptic problems
-
P. S. Vassilevski and R. Lazarov, Preconditioning mixed finite element saddle-point elliptic problems, Numer. Linear Algebra Appl., 3 (1996), pp. 1-20.
-
(1996)
Numer. Linear Algebra Appl.
, vol.3
, pp. 1-20
-
-
Vassilevski, P.S.1
Lazarov, R.2
-
36
-
-
34548307019
-
Preconditioning and convergence in the right norm
-
A. Wathen, Preconditioning and convergence in the right norm, Int. J. Comput. Math., 84 (2007), pp. 1199-1209.
-
(2007)
Int. J. Comput. Math.
, vol.84
, pp. 1199-1209
-
-
Wathen, A.1
-
37
-
-
0037249229
-
The Wiener-Askey polynomial chaos for stochastic differential equations
-
D. Xiu and G. E. Karniadakis, The Wiener-Askey polynomial chaos for stochastic differential equations, SIAM J. Sci. Comput., 24 (2002), pp. 619-644.
-
(2002)
SIAM J. Sci. Comput.
, vol.24
, pp. 619-644
-
-
Xiu, D.1
Karniadakis, G.E.2
|