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Volumn 66, Issue 12, 2006, Pages 1934-1954

A concurrent model reduction approach on spatial and random domains for the solution of stochastic PDEs

Author keywords

Flow in porous media; Karhunen Lo ve expansion; Model reduction; Proper orthogonal decomposition; Spectral stochastic finite element method; Stochastic partial differential equations; Uncertainty

Indexed keywords

FINITE ELEMENT METHOD; MATHEMATICAL MODELS; PARTIAL DIFFERENTIAL EQUATIONS; POLYNOMIALS; POROSITY; POROUS MATERIALS; RANDOM PROCESSES;

EID: 33745438681     PISSN: 00295981     EISSN: 10970207     Source Type: Journal    
DOI: 10.1002/nme.1611     Document Type: Article
Times cited : (21)

References (37)
  • 5
    • 0038115617 scopus 로고    scopus 로고
    • Inelastic deformation processes with random parameters: Methods of analysis and design
    • Doltsinis I. Inelastic deformation processes with random parameters: methods of analysis and design. Computer Methods in Applied Mechanics and Engineering 2003; 192:2405-2423.
    • (2003) Computer Methods in Applied Mechanics and Engineering , vol.192 , pp. 2405-2423
    • Doltsinis, I.1
  • 6
    • 0035424496 scopus 로고    scopus 로고
    • Parametric uncertainty analysis for thermal fluid calculations
    • Borggaard J, Pelletier D, Turgeon E. Parametric uncertainty analysis for thermal fluid calculations. Nonlinear Analysis 2001; 47:4533-4543.
    • (2001) Nonlinear Analysis , vol.47 , pp. 4533-4543
    • Borggaard, J.1    Pelletier, D.2    Turgeon, E.3
  • 11
    • 8744267721 scopus 로고    scopus 로고
    • Stochastic modeling of flow-structure interactions using generalized polynomial chaos
    • Xiu D, Lucor D, Su C-H, Kamiadakis GE. Stochastic modeling of flow-structure interactions using generalized polynomial chaos. Journal of Fluids Engineering 2001; 125:51-59.
    • (2001) Journal of Fluids Engineering , vol.125 , pp. 51-59
    • Xiu, D.1    Lucor, D.2    Su, C.-H.3    Kamiadakis, G.E.4
  • 12
    • 0037184252 scopus 로고    scopus 로고
    • Modeling uncertainty in steady state diffusion problems via generalized polynomial chaos
    • Xiu D, Kamiadakis GE. Modeling uncertainty in steady state diffusion problems via generalized polynomial chaos. Computer Methods in Applied Mechanics and Engineering 2002; 191:4927-4948.
    • (2002) Computer Methods in Applied Mechanics and Engineering , vol.191 , pp. 4927-4948
    • Xiu, D.1    Kamiadakis, G.E.2
  • 13
    • 0037408312 scopus 로고    scopus 로고
    • Modeling uncertainty in flow simulations via generalized polynomial chaos
    • Xiu D, Kamiadakis GE. Modeling uncertainty in flow simulations via generalized polynomial chaos. Journal of Computational Physics 2003; 187:137-167.
    • (2003) Journal of Computational Physics , vol.187 , pp. 137-167
    • Xiu, D.1    Kamiadakis, G.E.2
  • 14
    • 0141792397 scopus 로고    scopus 로고
    • A new stochastic approach to transient heat conduction modeling with uncertainty
    • Xiu D, Kamiadakis GE. A new stochastic approach to transient heat conduction modeling with uncertainty. International Journal of Heat and Mass Transfer 2003; 46:4681-4693.
    • (2003) International Journal of Heat and Mass Transfer , vol.46 , pp. 4681-4693
    • Xiu, D.1    Kamiadakis, G.E.2
  • 16
    • 0032496593 scopus 로고    scopus 로고
    • Probabilistic characterization of transport in heterogeneous porous media
    • Ghanem RG. Probabilistic characterization of transport in heterogeneous porous media. Computer Methods in Applied Mechanics and Engineering 1998; 158:199-220.
    • (1998) Computer Methods in Applied Mechanics and Engineering , vol.158 , pp. 199-220
    • Ghanem, R.G.1
  • 19
    • 8744246329 scopus 로고    scopus 로고
    • Variational multiscale stabilized FEM formulations for transport equations: Stochastic advection-diffusion and incompressible stochastic Navier-Stokes equations
    • Velamur Asokan B, Zabaras N. Variational multiscale stabilized FEM formulations for transport equations: stochastic advection-diffusion and incompressible stochastic Navier-Stokes equations. Journal of Computational Physics 2005; 202:94-133.
    • (2005) Journal of Computational Physics , vol.202 , pp. 94-133
    • Velamur Asokan, B.1    Zabaras, N.2
  • 20
  • 21
    • 0002708045 scopus 로고
    • The structure of inhomogeneous turbulence
    • Yaglom AM, Tatarski VI (eds). Nauka: Moscow
    • Lumley JL. The structure of inhomogeneous turbulence. In Atmospheric Turbulence and Radio Wave Propagation, Yaglom AM, Tatarski VI (eds). Nauka: Moscow, 1967; 166-178.
    • (1967) Atmospheric Turbulence and Radio Wave Propagation , pp. 166-178
    • Lumley, J.L.1
  • 22
    • 12044259644 scopus 로고
    • The proper orthogonal decomposition in the analysis of turbulent flows
    • Lumley JL. The proper orthogonal decomposition in the analysis of turbulent flows. Annual Review of Fluid Mechanics 1993; 25:539-575.
    • (1993) Annual Review of Fluid Mechanics , vol.25 , pp. 539-575
    • Lumley, J.L.1
  • 23
    • 0141892768 scopus 로고    scopus 로고
    • A proper orthogonal decomposition approach to microstructure model reduction in Rodrigues space with applications to the control of material properties
    • Acharjee S, Zabaras N. A proper orthogonal decomposition approach to microstructure model reduction in Rodrigues space with applications to the control of material properties. Computer Methods in Applied Mechanics and Engineering 2003; 51:5627-5646.
    • (2003) Computer Methods in Applied Mechanics and Engineering , vol.51 , pp. 5627-5646
    • Acharjee, S.1    Zabaras, N.2
  • 24
    • 4544308955 scopus 로고    scopus 로고
    • Design across length scales: A reduced-order model of polycrystal plasticity for the control of microstructure-sensitive material properties
    • Ganapathysubramanian S, Zabaras N. Design across length scales: a reduced-order model of polycrystal plasticity for the control of microstructure-sensitive material properties. Computer Methods in Applied Mechanics and Engineering 2004; 193:5017-5034.
    • (2004) Computer Methods in Applied Mechanics and Engineering , vol.193 , pp. 5017-5034
    • Ganapathysubramanian, S.1    Zabaras, N.2
  • 25
    • 0034327551 scopus 로고    scopus 로고
    • A reduced-order approach for optimal control of fluids using proper orthogonal decomposition
    • Ravindran SS. A reduced-order approach for optimal control of fluids using proper orthogonal decomposition. International Journal for Numerical Methods in Fluids 2000; 34:425-448.
    • (2000) International Journal for Numerical Methods in Fluids , vol.34 , pp. 425-448
    • Ravindran, S.S.1
  • 26
    • 0036447609 scopus 로고    scopus 로고
    • Adaptive reduced-order controllers for a thermal flow system using proper orthogonal decomposition
    • Ravindran SS. Adaptive reduced-order controllers for a thermal flow system using proper orthogonal decomposition. SIAM Journal on Scientific Computing 2002; 23:1924-1942.
    • (2002) SIAM Journal on Scientific Computing , vol.23 , pp. 1924-1942
    • Ravindran, S.S.1
  • 27
    • 0035067637 scopus 로고    scopus 로고
    • The influence of control on proper orthogonal decomposition of wall-bounded turbulent flows
    • Prabhu RD, Collis SS, Chang Y. The influence of control on proper orthogonal decomposition of wall-bounded turbulent flows. Physics of Fluids 2001; 13:520-537.
    • (2001) Physics of Fluids , vol.13 , pp. 520-537
    • Prabhu, R.D.1    Collis, S.S.2    Chang, Y.3
  • 28
    • 0035176703 scopus 로고    scopus 로고
    • Modeling and control of physical processes using proper orthogonal decomposition
    • Trans HT, Ly HV. Modeling and control of physical processes using proper orthogonal decomposition. Mathematical and Computer Modelling 2001; 33:223-236.
    • (2001) Mathematical and Computer Modelling , vol.33 , pp. 223-236
    • Trans, H.T.1    Ly, H.V.2
  • 31
    • 0037249229 scopus 로고    scopus 로고
    • The Wiener-Askey polynomial chaos for stochastic differential equations
    • Xiu D, Kamiadakis GE. The Wiener-Askey polynomial chaos for stochastic differential equations. SIAM Journal on Scientific Computing 2002; 24:619-644.
    • (2002) SIAM Journal on Scientific Computing , vol.24 , pp. 619-644
    • Xiu, D.1    Kamiadakis, G.E.2
  • 32
    • 19044387138 scopus 로고    scopus 로고
    • Using stochastic analysis to capture unstable equilibrium in natural convection
    • Velamur Asokan B, Zabaras N. Using stochastic analysis to capture unstable equilibrium in natural convection. Journal of Computational Physics 2005; 208:134-153.
    • (2005) Journal of Computational Physics , vol.208 , pp. 134-153
    • Velamur Asokan, B.1    Zabaras, N.2
  • 34
    • 4444235741 scopus 로고    scopus 로고
    • A stabilized volume-averaging finite element method for flow in porous media and binary alloy solidification processes
    • Zabaras N, Samanta D. A stabilized volume-averaging finite element method for flow in porous media and binary alloy solidification processes. International Journal for Numerical Methods in Engineering 2004; 60:1103-1138.
    • (2004) International Journal for Numerical Methods in Engineering , vol.60 , pp. 1103-1138
    • Zabaras, N.1    Samanta, D.2
  • 37
    • 84900847494 scopus 로고
    • Small sample sensitivity analysis techniques for computer models, with a application to risk assessment
    • Iman RL, Conover WJ. Small sample sensitivity analysis techniques for computer models, with a application to risk assessment. Communications in Statistics 1980; A9:1749-1842.
    • (1980) Communications in Statistics , vol.A9 , pp. 1749-1842
    • Iman, R.L.1    Conover, W.J.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.