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Volumn 5, Issue , 2004, Pages 15-24

Modeling uncertainty in three-dimensional heat transfer problems

Author keywords

Heat conduction; Polynomial chaos; Uncertainty

Indexed keywords

BOUNDARY CONDITIONS; CHAOS THEORY; COMPUTER SIMULATION; GALERKIN METHODS; MATHEMATICAL MODELS; POLYNOMIAL APPROXIMATION; PROBABILITY DISTRIBUTIONS; PROBLEM SOLVING; RANDOM PROCESSES; THERMAL CONDUCTIVITY; VECTORS;

EID: 4644275414     PISSN: 14626063     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper
Times cited : (1)

References (25)
  • 1
    • 0000786435 scopus 로고
    • The homogeneous chaos
    • Wiener, N., The homogeneous chaos. Amer J Math, 60, pp. 897-936,1938.
    • (1938) Amer J Math , vol.60 , pp. 897-936
    • Wiener, N.1
  • 3
    • 0022719849 scopus 로고
    • Probabilistic finite elements for nonlinear structural dynamics
    • Liu, W.K., Belytschko, T. & Mani, A., Probabilistic finite elements for nonlinear structural dynamics. Comput Methods Appl Mech Engrg, 56, pp. 6181, 1986.
    • (1986) Comput Methods Appl Mech Engrg , vol.56 , pp. 6181
    • Liu, W.K.1    Belytschko, T.2    Mani, A.3
  • 5
    • 0020842793 scopus 로고
    • Stochastic finite element analysis of simple beams
    • Vanmarcke, E.H. & Grigoriu, M., Stochastic finite element analysis of simple beams. J Eng Mech, 109(5), pp. 1203-1214, 1983.
    • (1983) J Eng Mech , vol.109 , Issue.5 , pp. 1203-1214
    • Vanmarcke, E.H.1    Grigoriu, M.2
  • 6
    • 0023980492 scopus 로고
    • Response variability of stochastic finite element systems
    • Shinozuka, M. & Deodatis, G., Response variability of stochastic finite element systems. J Eng Mech, 114(3), pp. 499-519, 1988.
    • (1988) J Eng Mech , vol.114 , Issue.3 , pp. 499-519
    • Shinozuka, M.1    Deodatis, G.2
  • 7
    • 0024067174 scopus 로고
    • Neumann expansion for stochastic finite element analysis
    • Yamazaki, F., Shinozuka, M. & Dasgupta, G., Neumann expansion for stochastic finite element analysis. J Eng Mech, 114(8), pp. 1335-1354, 1988.
    • (1988) J Eng Mech , vol.114 , Issue.8 , pp. 1335-1354
    • Yamazaki, F.1    Shinozuka, M.2    Dasgupta, G.3
  • 8
    • 0026836202 scopus 로고
    • Stochastic FEM based on local average of random vector fields
    • Zhu, W.Q., Ren, Y.J. & Wu, W.Q., Stochastic FEM based on local average of random vector fields. J Eng Mech, 118(3), pp. 496-511, 1992.
    • (1992) J Eng Mech , vol.118 , Issue.3 , pp. 496-511
    • Zhu, W.Q.1    Ren, Y.J.2    Wu, W.Q.3
  • 9
    • 0026204804 scopus 로고
    • Weighted integral method. I: Stochastic stiffness matrix
    • Deodatis, G., Weighted integral method. I: stochastic stiffness matrix. J Eng Mech, 117(8), pp. 1851-1864, 1991.
    • (1991) J Eng Mech , vol.117 , Issue.8 , pp. 1851-1864
    • Deodatis, G.1
  • 10
    • 0026204584 scopus 로고
    • Weighted integral method. II: Response variability and reliability
    • Deodatis, G. & Shinozuka, M., Weighted integral method. II: response variability and reliability. J Eng Mech, 117(8), pp. 1865-1877, 1991.
    • (1991) J Eng Mech , vol.117 , Issue.8 , pp. 1865-1877
    • Deodatis, G.1    Shinozuka, M.2
  • 12
    • 13844312442 scopus 로고    scopus 로고
    • Stochastic finite elements for heterogeneous media with multiple random non-gaussian properties
    • Ghanem, R.G., Stochastic finite elements for heterogeneous media with multiple random non-gaussian properties. ASCE J Engrg Mech, 125(1), pp. 2640, 1999.
    • (1999) ASCE J Engrg Mech , vol.125 , Issue.1 , pp. 2640
    • Ghanem, R.G.1
  • 13
    • 0033329066 scopus 로고    scopus 로고
    • Propagation of uncertainty in complex physical systems using a stochastic finite elements approach
    • Ghanem, R.G. & Red-Horse, J., Propagation of uncertainty in complex physical systems using a stochastic finite elements approach. Physica D, 133, pp. 137-144, 1999.
    • (1999) Physica D , vol.133 , pp. 137-144
    • Ghanem, R.G.1    Red-Horse, J.2
  • 14
    • 0033528038 scopus 로고    scopus 로고
    • Ingredients for a general purpose stochastic finite element formulation
    • Ghanem, R.G., Ingredients for a general purpose stochastic finite element formulation. Comput Methods Appl Mech Engrg, 168, pp. 19-34, 1999.
    • (1999) Comput Methods Appl Mech Engrg , vol.168 , pp. 19-34
    • Ghanem, R.G.1
  • 15
    • 0037249229 scopus 로고    scopus 로고
    • The wiener-askey polynomial chaos for stochastic differential equations
    • Xiu, D. & Karniadarkis, G.E., The Wiener-Askey polynomial chaos for stochastic differential equations. SIAM J Sci Comput, 24(2), pp. 619-644, 2002.
    • (2002) SIAM J Sci Comput , vol.24 , Issue.2 , pp. 619-644
    • Xiu, D.1    Karniadarkis, G.E.2
  • 16
    • 0037184252 scopus 로고    scopus 로고
    • Modeling uncertainty in steady state diffusion problems via generalized polynomial chaos
    • Xiu, D. & Karniadarkis, G.E., Modeling uncertainty in steady state diffusion problems via generalized polynomial chaos. Comput Methods Appl Math Eng, 191, pp. 4927-4948, 2002.
    • (2002) Comput Methods Appl Math Eng , vol.191 , pp. 4927-4948
    • Xiu, D.1    Karniadarkis, G.E.2
  • 17
    • 0037408312 scopus 로고    scopus 로고
    • Modeling uncertainty in flow simulations via generalized polynomial chaos
    • Xiu, D. & Karniadakis, G., Modeling uncertainty in flow simulations via generalized polynomial chaos. J Comput Phys, 187, pp. 137-167, 2003.
    • (2003) J Comput Phys , vol.187 , pp. 137-167
    • Xiu, D.1    Karniadakis, G.2
  • 18
    • 0037119496 scopus 로고    scopus 로고
    • On solving elliptic stochastic partial differential equations
    • Babuška, I. & Chatzipantelidis, P., On solving elliptic stochastic partial differential equations. Comput Methods Appl Mech Engrg, 191, pp. 4093-4122, 2002.
    • (2002) Comput Methods Appl Mech Engrg , vol.191 , pp. 4093-4122
    • Babuška, I.1    Chatzipantelidis, P.2
  • 19
    • 3242735138 scopus 로고    scopus 로고
    • Galerkin finite element approximations of stochastic elliptic differential equations
    • Technical Report 02-38, TICAM
    • Babuška, I, Tempone, R. & Zouraris, G.E., Galerkin finite element approximations of stochastic elliptic differential equations. Technical Report 02-38, TICAM, 2002.
    • (2002) Technical Report
    • Babuška, I.1    Tempone, R.2    Zouraris, G.E.3
  • 20
    • 0035964634 scopus 로고    scopus 로고
    • Solution of stochastic partial differential equations using Galerkin finite element techniques
    • Deb, M.K., Babuška, I. & Oden, J.T., Solution of stochastic partial differential equations using Galerkin finite element techniques. Comput Methods Appl Mech Engrg, 190, pp. 6359-6372, 2001.
    • (2001) Comput Methods Appl Mech Engrg , vol.190 , pp. 6359-6372
    • Deb, M.K.1    Babuška, I.2    Oden, J.T.3
  • 24
    • 0030502142 scopus 로고    scopus 로고
    • Deflation techniques for an implicitly restarted Arnoldi iteration
    • Lehoucq, R.B. & Sorensen, D.C., Deflation techniques for an implicitly restarted Arnoldi iteration. SIAM Matrix Analysis and Applications, 17(4), pp. 789-821, 1996.
    • (1996) SIAM Matrix Analysis and Applications , vol.17 , Issue.4 , pp. 789-821
    • Lehoucq, R.B.1    Sorensen, D.C.2
  • 25
    • 0141792397 scopus 로고    scopus 로고
    • A new stochastic approach to transient heat conduction modeling with uncertainty
    • Xiu, D. & Karniadarkis, G.E., A new stochastic approach to transient heat conduction modeling with uncertainty. Int J Heat Mass Trans, 46(24), pp. 4681-4693, 2003.
    • (2003) Int J Heat Mass Trans , vol.46 , Issue.24 , pp. 4681-4693
    • Xiu, D.1    Karniadarkis, G.E.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.