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Volumn 197, Issue 17-18, 2008, Pages 1495-1506

Multi-element stochastic reduced basis methods

Author keywords

Heat transfer; Preconditioning; Stochastic partial differential equations; Stochastic reduced basis methods; Uncertainty quantification

Indexed keywords

BOUNDARY CONDITIONS; CONVERGENCE OF NUMERICAL METHODS; HEAT TRANSFER; NUMERICAL METHODS; PARTIAL DIFFERENTIAL EQUATIONS; STATISTICS;

EID: 39149121827     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2007.11.021     Document Type: Article
Times cited : (21)

References (27)
  • 1
    • 0000786435 scopus 로고
    • The homogeneous chaos
    • Wiener N. The homogeneous chaos. Am. J. Math. 60 (1938) 897-936
    • (1938) Am. J. Math. , vol.60 , pp. 897-936
    • Wiener, N.1
  • 2
    • 0000148817 scopus 로고
    • The orthogonal development of nonlinear functionals in series of Fourier-Hermite functionals
    • Cameron R.H., and Martin W.T. The orthogonal development of nonlinear functionals in series of Fourier-Hermite functionals. Annal. Math. 48 (1947) 385-392
    • (1947) Annal. Math. , vol.48 , pp. 385-392
    • Cameron, R.H.1    Martin, W.T.2
  • 4
    • 0027836627 scopus 로고
    • Stochastic Galerkin expansion for nonlinear random vibration analysis
    • Ghanem R., and Spanos P. Stochastic Galerkin expansion for nonlinear random vibration analysis. Probabilist. Engrg. Mech. 8 (1993) 255-264
    • (1993) Probabilist. Engrg. Mech. , vol.8 , pp. 255-264
    • Ghanem, R.1    Spanos, P.2
  • 5
    • 0030318028 scopus 로고    scopus 로고
    • Stochastic finite element analysis of randomly layered media
    • Ghanem R., and Brzkala V. Stochastic finite element analysis of randomly layered media. J. Engrg. Mech. 122 (1996) 361-369
    • (1996) J. Engrg. Mech. , vol.122 , pp. 361-369
    • Ghanem, R.1    Brzkala, V.2
  • 6
    • 0032496593 scopus 로고    scopus 로고
    • Probabilistic characterization of transport in heterogeneous media
    • Ghanem R. Probabilistic characterization of transport in heterogeneous media. Comput. Meth. Appl. Mech. Engrg. 158 (1998) 199-220
    • (1998) Comput. Meth. Appl. Mech. Engrg. , vol.158 , pp. 199-220
    • Ghanem, R.1
  • 7
    • 0035506770 scopus 로고    scopus 로고
    • A stochastic projection method for fluid flow; basic formulation
    • Maître O.L., Reagan M., Najm H., Ghanem R., and Knio O. A stochastic projection method for fluid flow; basic formulation. J. Comput. Phys. 173 (2001) 481-511
    • (2001) J. Comput. Phys. , vol.173 , pp. 481-511
    • Maître, O.L.1    Reagan, M.2    Najm, H.3    Ghanem, R.4    Knio, O.5
  • 8
    • 0037159819 scopus 로고    scopus 로고
    • Mid-frequency structural dynamics with parameter uncertainity
    • Sarkar A., and Ghanem R. Mid-frequency structural dynamics with parameter uncertainity. Comput. Meth. Appl. Mech. Engrg. 191 (2002) 5499-5513
    • (2002) Comput. Meth. Appl. Mech. Engrg. , vol.191 , pp. 5499-5513
    • Sarkar, A.1    Ghanem, R.2
  • 9
    • 0033334624 scopus 로고    scopus 로고
    • Stochastic finite element method for elasto-plastic body
    • Anders M., and Hori M. Stochastic finite element method for elasto-plastic body. Int. J. Numer. Methods Engrg. 46 (1999) 1897-1916
    • (1999) Int. J. Numer. Methods Engrg. , vol.46 , pp. 1897-1916
    • Anders, M.1    Hori, M.2
  • 10
    • 0037303227 scopus 로고    scopus 로고
    • A Green's function method to SH-wave motion in random continuum
    • Manolis G.D., and Karakostas C.Z. A Green's function method to SH-wave motion in random continuum. Engrg. Anal. Bound. Elem. 27 (2003) 93-100
    • (2003) Engrg. Anal. Bound. Elem. , vol.27 , pp. 93-100
    • Manolis, G.D.1    Karakostas, C.Z.2
  • 11
    • 0037249229 scopus 로고    scopus 로고
    • The Wiener-Askey polynomial chaos for stochastic differential equations
    • Xiu D., and Karniadakis G.E. The Wiener-Askey polynomial chaos for stochastic differential equations. SIAM J. Sci. Comput. 24 2 (2002) 619-644
    • (2002) SIAM J. Sci. Comput. , vol.24 , Issue.2 , pp. 619-644
    • Xiu, D.1    Karniadakis, G.E.2
  • 12
    • 0037408312 scopus 로고    scopus 로고
    • Modelling uncertainity in flow simulations via generalized polynomial chaos
    • Xiu D., and Karniadakis G.E. Modelling uncertainity in flow simulations via generalized polynomial chaos. J. Comput. Phys. 187 (2003) 137-167
    • (2003) J. Comput. Phys. , vol.187 , pp. 137-167
    • Xiu, D.1    Karniadakis, G.E.2
  • 14
    • 3242712896 scopus 로고    scopus 로고
    • Multi-resolution analysis of Wiener-type uncertainity propagation schemes
    • Maître O.P.L., Njam H.N., Ghanem R.G., and Knio O.M. Multi-resolution analysis of Wiener-type uncertainity propagation schemes. J. Comput. Phys. 197 (2004) 502-531
    • (2004) J. Comput. Phys. , vol.197 , pp. 502-531
    • Maître, O.P.L.1    Njam, H.N.2    Ghanem, R.G.3    Knio, O.M.4
  • 15
    • 13844319204 scopus 로고    scopus 로고
    • Galerkin finite element approximations of stochastic elliptic partial differential equations
    • Babuška I., Tempone R., and Zouraris E. Galerkin finite element approximations of stochastic elliptic partial differential equations. SIAM J. Numer. Anal. 42 (2004) 800-825
    • (2004) SIAM J. Numer. Anal. , vol.42 , pp. 800-825
    • Babuška, I.1    Tempone, R.2    Zouraris, E.3
  • 16
    • 85067316737 scopus 로고    scopus 로고
    • P.B. Nair, On the theoretical foundations of stochastic reduced basis methods, in: Proceedings of 42nd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, AIAA Paper No. 2001-1677, Seattle WA, 2001.
    • P.B. Nair, On the theoretical foundations of stochastic reduced basis methods, in: Proceedings of 42nd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, AIAA Paper No. 2001-1677, Seattle WA, 2001.
  • 17
    • 0036684042 scopus 로고    scopus 로고
    • Stochastic reduced basis methods
    • Nair P.B., and Keane A.J. Stochastic reduced basis methods. AIAA J. 40 (2002) 1653-1664
    • (2002) AIAA J. , vol.40 , pp. 1653-1664
    • Nair, P.B.1    Keane, A.J.2
  • 18
    • 33644608285 scopus 로고    scopus 로고
    • Comparative study of projection schemes for stochastic finite element analysis
    • Sachdeva S.K., Nair P.B., and Keane A.J. Comparative study of projection schemes for stochastic finite element analysis. Comput. Methods Appl. Mech. Engrg. 195 (2006) 2371-2392
    • (2006) Comput. Methods Appl. Mech. Engrg. , vol.195 , pp. 2371-2392
    • Sachdeva, S.K.1    Nair, P.B.2    Keane, A.J.3
  • 19
    • 33644888792 scopus 로고    scopus 로고
    • Hybridization of stochastic reduced basis methods with polynomial chaos expansions
    • Sachdeva S.K., Nair P.B., and Keane A.J. Hybridization of stochastic reduced basis methods with polynomial chaos expansions. Probabilist. Engrg. Mech. 21 (2006) 182-192
    • (2006) Probabilist. Engrg. Mech. , vol.21 , pp. 182-192
    • Sachdeva, S.K.1    Nair, P.B.2    Keane, A.J.3
  • 20
    • 84986296677 scopus 로고    scopus 로고
    • A two-scale non-perturbative approach to uncertainity analysis of diffusion in random composites
    • Xiu D., and Tartakovsky D.M. A two-scale non-perturbative approach to uncertainity analysis of diffusion in random composites. SIAM J. Multiscale Modell. Simulat. 2 4 (2004) 662-674
    • (2004) SIAM J. Multiscale Modell. Simulat. , vol.2 , Issue.4 , pp. 662-674
    • Xiu, D.1    Tartakovsky, D.M.2
  • 21
    • 21444449245 scopus 로고    scopus 로고
    • An adaptive multi-element generalized polynomial chaos method for stochastic differential equations
    • Wan X., and Karniadakis G.E. An adaptive multi-element generalized polynomial chaos method for stochastic differential equations. J. Comput. Phys. 209 (2005) 617-642
    • (2005) J. Comput. Phys. , vol.209 , pp. 617-642
    • Wan, X.1    Karniadakis, G.E.2
  • 22
    • 33749326978 scopus 로고    scopus 로고
    • Multi-element generalized polynomial chaos for arbitrary probability measures
    • Wan X., and Karniadakis G.E. Multi-element generalized polynomial chaos for arbitrary probability measures. SIAM J. Sci. Comput. 28 3 (2006) 901-928
    • (2006) SIAM J. Sci. Comput. , vol.28 , Issue.3 , pp. 901-928
    • Wan, X.1    Karniadakis, G.E.2
  • 23
    • 39149094987 scopus 로고    scopus 로고
    • Multi-resolution analysis for uncertainty quantification in chemical systems
    • Maître O.L., Najm H., Pébay P., Ghanem R., and Knio O. Multi-resolution analysis for uncertainty quantification in chemical systems. SIAM J. Sci. Comput. 29 2 (2007) 864-889
    • (2007) SIAM J. Sci. Comput. , vol.29 , Issue.2 , pp. 864-889
    • Maître, O.L.1    Najm, H.2    Pébay, P.3    Ghanem, R.4    Knio, O.5
  • 24
    • 39149109984 scopus 로고    scopus 로고
    • Projection schemes in stochastic finite element analysis
    • Nikolaidis E., Ghiocel D.M., and Singhal S. (Eds), CRC Press (Chapter 21).
    • Nair P.B. Projection schemes in stochastic finite element analysis. In: Nikolaidis E., Ghiocel D.M., and Singhal S. (Eds). Engineering Design and Reliability: Handbook (2005), CRC Press (Chapter 21).
    • (2005) Engineering Design and Reliability: Handbook
    • Nair, P.B.1
  • 25
    • 0037184252 scopus 로고    scopus 로고
    • Modelling uncertainty in steady state diffusion problems via generalized polynomial chaos
    • Xiu D., and Karniadakis G.E. Modelling uncertainty in steady state diffusion problems via generalized polynomial chaos. Comput. Methods Appl. Mech. Engrg. 191 (2002) 4927-4948
    • (2002) Comput. Methods Appl. Mech. Engrg. , vol.191 , pp. 4927-4948
    • Xiu, D.1    Karniadakis, G.E.2
  • 26
    • 39149138164 scopus 로고    scopus 로고
    • A. Keese, Numerical solution of systems with stochastic uncertainties - a general purpose framework for stochastic finite elements, Ph.D. thesis, Technische Universitat Braunschweig, Brunswick, 2004.
    • A. Keese, Numerical solution of systems with stochastic uncertainties - a general purpose framework for stochastic finite elements, Ph.D. thesis, Technische Universitat Braunschweig, Brunswick, 2004.
  • 27
    • 39149112550 scopus 로고    scopus 로고
    • D. Darmofal, Steady and transient heat transfer simulation of a turbine blade, Tech. rep., MIT. , 2005.
    • D. Darmofal, Steady and transient heat transfer simulation of a turbine blade, Tech. rep., MIT. , 2005.


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.