메뉴 건너뛰기




Volumn 198, Issue 21-26, 2009, Pages 1926-1934

Reduced Chaos decomposition with random coefficients of vector-valued random variables and random fields

Author keywords

Karhunen Loeve; Polynomial Chaos; Stochastic model reduction; Uncertainty quantification

Indexed keywords

COARSE-SCALE MODELS; EPISTEMIC UNCERTAINTIES; FUNCTIONAL REPRESENTATIONS; KARHUNEN-LOEVE; KARHUNEN-LOEVE EXPANSIONS; MODELING ERRORS; POLYNOMIAL CHAOS; POLYNOMIAL CHAOS DECOMPOSITIONS; RANDOM COEFFICIENTS; RANDOM FIELDS; RANDOM FUNCTIONS; STOCHASTIC MODEL REDUCTION; UNCERTAINTY QUANTIFICATION; VECTOR-VALUED;

EID: 63449094428     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2008.12.035     Document Type: Article
Times cited : (47)

References (23)
  • 1
    • 48849110024 scopus 로고    scopus 로고
    • Probabilistic equivalence and stochastic model reduction in multiscale analysis
    • Aarnst M., and Ghanem R. Probabilistic equivalence and stochastic model reduction in multiscale analysis. Comput. Methods Appl. Mech. Engrg. 197 43-44 (2008) 3584-3592
    • (2008) Comput. Methods Appl. Mech. Engrg. , vol.197 , Issue.43-44 , pp. 3584-3592
    • Aarnst, M.1    Ghanem, R.2
  • 2
    • 8744246329 scopus 로고    scopus 로고
    • Variational multiscale stabilized FEM formulations for transport equations: stochastic advection-diffusion and incompressible stochastic Navier-Stokes equations
    • Asokan V., Narayanan B., and Zabaras N. Variational multiscale stabilized FEM formulations for transport equations: stochastic advection-diffusion and incompressible stochastic Navier-Stokes equations. J. Comput. Phys. 202 1 (2005) 94-133
    • (2005) J. Comput. Phys. , vol.202 , Issue.1 , pp. 94-133
    • Asokan, V.1    Narayanan, B.2    Zabaras, N.3
  • 3
    • 13844319204 scopus 로고    scopus 로고
    • Galerkin finite element approximations of stochastic elliptic partial differential equations
    • Babuska I., Tempone R., and Zouraris G.E. Galerkin finite element approximations of stochastic elliptic partial differential equations. SIAM J. Numer. Anal. 42 2 (2004) 800-825
    • (2004) SIAM J. Numer. Anal. , vol.42 , Issue.2 , pp. 800-825
    • Babuska, I.1    Tempone, R.2    Zouraris, G.E.3
  • 4
    • 55349148993 scopus 로고    scopus 로고
    • Asymptotic sampling distribution for polynomial Chaos representation of data: a maximum-entropy and Fisher information approach
    • Das S., Ghanem R., and Spall J. Asymptotic sampling distribution for polynomial Chaos representation of data: a maximum-entropy and Fisher information approach. SIAM J. Sci. Comput. 30 5 (2008) 2207-2234
    • (2008) SIAM J. Sci. Comput. , vol.30 , Issue.5 , pp. 2207-2234
    • Das, S.1    Ghanem, R.2    Spall, J.3
  • 5
    • 63449133296 scopus 로고    scopus 로고
    • Sonjoy Das, Roger Ghanem, Hybrid representations for complex dynamical stochastic systems: coupled non-parametric and parametric models, in: C. Soize, G.I. Schuller (Eds.), Proceedings of the Sixth International Conference on Structural Dynamics, Paris, France, 4-7 September 2005, pp. v.1, 53-60.
    • Sonjoy Das, Roger Ghanem, Hybrid representations for complex dynamical stochastic systems: coupled non-parametric and parametric models, in: C. Soize, G.I. Schuller (Eds.), Proceedings of the Sixth International Conference on Structural Dynamics, Paris, France, 4-7 September 2005, pp. v.1, 53-60.
  • 6
    • 33646514831 scopus 로고    scopus 로고
    • Maximum likelihood estimation of stochastic Chaos representation from experimental data
    • Descelliers C., Soize C., and Ghanem R. Maximum likelihood estimation of stochastic Chaos representation from experimental data. Int. J. Numer. Methods Engrg. 66 6 (2006) 978-1001
    • (2006) Int. J. Numer. Methods Engrg. , vol.66 , Issue.6 , pp. 978-1001
    • Descelliers, C.1    Soize, C.2    Ghanem, R.3
  • 7
    • 10444261986 scopus 로고    scopus 로고
    • Finite elements for elliptic problems with stochastic coefficients
    • Frauenfelder P., Schwab C., and Todor R.A. Finite elements for elliptic problems with stochastic coefficients. Comput. Methods Appl. Mech. Engrg. 194 2-5 (2005) 205-228
    • (2005) Comput. Methods Appl. Mech. Engrg. , vol.194 , Issue.2-5 , pp. 205-228
    • Frauenfelder, P.1    Schwab, C.2    Todor, R.A.3
  • 8
    • 0033528038 scopus 로고    scopus 로고
    • Ingredients for a general purpose stochastic finite elements formulation
    • Ghanem R. Ingredients for a general purpose stochastic finite elements formulation. Comput. Methods Appl. Mech. Engrg. 168 1-4 (1999) 19-34
    • (1999) Comput. Methods Appl. Mech. Engrg. , vol.168 , Issue.1-4 , pp. 19-34
    • Ghanem, R.1
  • 10
    • 33746495084 scopus 로고    scopus 로고
    • Characterization of stochastic system parameters from experimental data: a Bayesian inference approach
    • Ghanem R., and Doostan R. Characterization of stochastic system parameters from experimental data: a Bayesian inference approach. J. Comput. Phys. 217 1 (2006) 63-81
    • (2006) J. Comput. Phys. , vol.217 , Issue.1 , pp. 63-81
    • Ghanem, R.1    Doostan, R.2
  • 12
    • 51249164859 scopus 로고
    • On asymptotic properties of maximum likelihood estimators for parabolic stochastic pdes
    • Huebner M., and Rozovskii B. On asymptotic properties of maximum likelihood estimators for parabolic stochastic pdes. Probab. Theory Related Fields 103 (1995) 143-163
    • (1995) Probab. Theory Related Fields , vol.103 , pp. 143-163
    • Huebner, M.1    Rozovskii, B.2
  • 13
    • 3242712896 scopus 로고    scopus 로고
    • Multi-resolution analysis of Wiener-type uncertainty propagation schemes
    • Le Maitre O.P., Najm H., Ghanem R., and Knio O. Multi-resolution analysis of Wiener-type uncertainty propagation schemes. J. Comput. Phys. 197 2 (2004) 502-531
    • (2004) J. Comput. Phys. , vol.197 , Issue.2 , pp. 502-531
    • Le Maitre, O.P.1    Najm, H.2    Ghanem, R.3    Knio, O.4
  • 14
    • 2942555049 scopus 로고    scopus 로고
    • Uncertainty propagation using Wiener-Haar expansions
    • Le Maitre O.P., Knio O., Najm H., and Ghanem R. Uncertainty propagation using Wiener-Haar expansions. J. Comput. Phys. 197 (2004) 28-57
    • (2004) J. Comput. Phys. , vol.197 , pp. 28-57
    • Le Maitre, O.P.1    Knio, O.2    Najm, H.3    Ghanem, R.4
  • 15
    • 13844308726 scopus 로고    scopus 로고
    • Galerkin methods for linear and nonlinear elliptic stochastic partial differential equations
    • Matthies H.G., and Keese A. Galerkin methods for linear and nonlinear elliptic stochastic partial differential equations. Comput. Methods Appl. Mech. Engrg. 194 12-16 (2005) 1295-1331
    • (2005) Comput. Methods Appl. Mech. Engrg. , vol.194 , Issue.12-16 , pp. 1295-1331
    • Matthies, H.G.1    Keese, A.2
  • 16
    • 63449137570 scopus 로고    scopus 로고
    • Uncertainty quantification and polynomial Chaos techniques in computational fluid dynamics
    • Najm H.N. Uncertainty quantification and polynomial Chaos techniques in computational fluid dynamics. Ann. Rev. Fluid Mech. 41 1 (2009)
    • (2009) Ann. Rev. Fluid Mech. , vol.41 , Issue.1
    • Najm, H.N.1
  • 17
    • 2642532808 scopus 로고    scopus 로고
    • A probabilistic approach to uncertainty quantification with limited information
    • Red-Horse J.R., and Benjamin A.S. A probabilistic approach to uncertainty quantification with limited information. Reliab. Engrg. Syst. Safety 85 (2004) 183-190
    • (2004) Reliab. Engrg. Syst. Safety , vol.85 , pp. 183-190
    • Red-Horse, J.R.1    Benjamin, A.S.2
  • 18
    • 0000848317 scopus 로고
    • The moment problem for polynomials forms in normal random variables
    • Slud E.V. The moment problem for polynomials forms in normal random variables. Ann. Probab. 21 4 (1993) 2200-2214
    • (1993) Ann. Probab. , vol.21 , Issue.4 , pp. 2200-2214
    • Slud, E.V.1
  • 19
    • 0037644831 scopus 로고    scopus 로고
    • Random matrix theory and non-parametric model of random uncertainties in vibration analysis
    • Soize C. Random matrix theory and non-parametric model of random uncertainties in vibration analysis. J. Sound Vib. 263 4 (2003) 893-916
    • (2003) J. Sound Vib. , vol.263 , Issue.4 , pp. 893-916
    • Soize, C.1
  • 20
    • 13844310464 scopus 로고    scopus 로고
    • Random matrix theory for modeling uncertainties in computational mechanics
    • Soize C. Random matrix theory for modeling uncertainties in computational mechanics. Comput. Methods Appl. Mech. Engrg. 194 12-16 (2005) 1333-1366
    • (2005) Comput. Methods Appl. Mech. Engrg. , vol.194 , Issue.12-16 , pp. 1333-1366
    • Soize, C.1
  • 21
    • 16244409214 scopus 로고    scopus 로고
    • Physical systems with random uncertainties: Chaos representations with arbitrary probability measure
    • Soize C., and Ghanem R. Physical systems with random uncertainties: Chaos representations with arbitrary probability measure. SIAM J. Sci. Comput. 26 2 (2004) 395-410
    • (2004) SIAM J. Sci. Comput. , vol.26 , Issue.2 , pp. 395-410
    • Soize, C.1    Ghanem, R.2
  • 22
    • 33749326978 scopus 로고    scopus 로고
    • Multi-element generalized polynomial Chaos for arbitrary probability measures
    • electronic
    • Wan X., and Karniadakis G.E. Multi-element generalized polynomial Chaos for arbitrary probability measures. SIAM J. Sci. Comput. 28 3 (2006) 901-928 electronic
    • (2006) SIAM J. Sci. Comput. , vol.28 , Issue.3 , pp. 901-928
    • Wan, X.1    Karniadakis, G.E.2
  • 23
    • 0037408312 scopus 로고    scopus 로고
    • Modeling uncertainty in flow simulations via generalized polynomial Chaos
    • Xiu D., and Karniadakis G. Modeling uncertainty in flow simulations via generalized polynomial Chaos. J. Comput. Phys. 187 1 (2003) 137-167
    • (2003) J. Comput. Phys. , vol.187 , Issue.1 , pp. 137-167
    • Xiu, D.1    Karniadakis, G.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.