Cluster-based generalized multiscale finite element method for elliptic PDEs with random coefficients

Chung, Eric T.; Efendiev, Yalchin; Leung, Wing Tat; Zhang, Zhiwen

doi:10.1016/j.jcp.2018.05.041

Title: Cluster-based generalized multiscale finite element method for elliptic PDEs with random coefficients

Journal Article · Mon Oct 01 00:00:00 EDT 2018 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2018.05.041· OSTI ID:1564505

Chung, Eric T.; Efendiev, Yalchin; Leung, Wing Tat;

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Sponsoring Organization:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)

Grant/Contract Number:: FG02-13ER26165; SC0010713

OSTI ID:: 1564505

Journal Information:: Journal of Computational Physics, Journal Name: Journal of Computational Physics Vol. 371 Journal Issue: C; ISSN 0021-9991

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 9 works

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References (27)

Uncertainty Quantification and Polynomial Chaos Techniques in Computational Fluid Dynamics Najm, Habib N. Annual Review of Fluid Mechanics, Vol. 41, Issue 1 https://doi.org/10.1146/annurev.fluid.010908.165248	journal	January 2009
Finding Structure with Randomness: Probabilistic Algorithms for Constructing Approximate Matrix Decompositions Halko, N.; Martinsson, P. G.; Tropp, J. A. SIAM Review, Vol. 53, Issue 2 https://doi.org/10.1137/090771806	journal	January 2011
Residual-driven online generalized multiscale finite element methods Chung, Eric T.; Efendiev, Yalchin; Leung, Wing Tat Journal of Computational Physics, Vol. 302 https://doi.org/10.1016/j.jcp.2015.07.068	journal	December 2015
Randomized algorithms for the low-rank approximation of matrices Liberty, E.; Woolfe, F.; Martinsson, P. -G. Proceedings of the National Academy of Sciences, Vol. 104, Issue 51 https://doi.org/10.1073/pnas.0709640104	journal	December 2007
Galerkin methods for linear and nonlinear elliptic stochastic partial differential equations Matthies, Hermann G.; Keese, Andreas Computer Methods in Applied Mechanics and Engineering, Vol. 194, Issue 12-16 https://doi.org/10.1016/j.cma.2004.05.027	journal	April 2005
Modeling uncertainty in flow simulations via generalized polynomial chaos Xiu, Dongbin; Karniadakis, George Em Journal of Computational Physics, Vol. 187, Issue 1 https://doi.org/10.1016/S0021-9991(03)00092-5	journal	May 2003
A Multiscale Finite Element Method for Elliptic Problems in Composite Materials and Porous Media Hou, Thomas Y.; Wu, Xiao-Hui Journal of Computational Physics, Vol. 134, Issue 1 https://doi.org/10.1006/jcph.1997.5682	journal	June 1997
An adaptive GMsFEM for high-contrast flow problems Chung, Eric T.; Efendiev, Yalchin; Li, Guanglian Journal of Computational Physics, Vol. 273 https://doi.org/10.1016/j.jcp.2014.05.007	journal	September 2014
Wiener Chaos expansions and numerical solutions of randomly forced equations of fluid mechanics Hou, Thomas Y.; Luo, Wuan; Rozovskii, Boris Journal of Computational Physics, Vol. 216, Issue 2 https://doi.org/10.1016/j.jcp.2006.01.008	journal	August 2006
A dynamically bi-orthogonal method for time-dependent stochastic partial differential equations II: Adaptivity and generalizations Cheng, Mulin; Hou, Thomas Y.; Zhang, Zhiwen Journal of Computational Physics, Vol. 242 https://doi.org/10.1016/j.jcp.2013.02.020	journal	June 2013
Adaptive multiscale model reduction with Generalized Multiscale Finite Element Methods Chung, Eric; Efendiev, Yalchin; Hou, Thomas Y. Journal of Computational Physics, Vol. 320 https://doi.org/10.1016/j.jcp.2016.04.054	journal	September 2016
Convergence of a Nonconforming Multiscale Finite Element Method Efendiev, Yalchin R.; Hou, Thomas Y.; Wu, Xiao-Hui SIAM Journal on Numerical Analysis, Vol. 37, Issue 3 https://doi.org/10.1137/S0036142997330329	journal	January 2000
Monte Carlo and quasi-Monte Carlo methods Caflisch, Russel E. Acta Numerica, Vol. 7 https://doi.org/10.1017/S0962492900002804	journal	January 1998
Randomized Oversampling for Generalized Multiscale Finite Element Methods Calo, Victor M.; Efendiev, Yalchin; Galvis, Juan Multiscale Modeling & Simulation, Vol. 14, Issue 1 https://doi.org/10.1137/140988826	journal	January 2016
A Data-Driven Stochastic Method for Elliptic PDEs with Random Coefficients Cheng, Mulin; Hou, Thomas Y.; Yan, Mike SIAM/ASA Journal on Uncertainty Quantification, Vol. 1, Issue 1 https://doi.org/10.1137/130913249	journal	January 2013
Multilevel Monte Carlo Path Simulation Giles, Michael B. Operations Research, Vol. 56, Issue 3 https://doi.org/10.1287/opre.1070.0496	journal	June 2008
Generalized multiscale finite element methods (GMsFEM) Efendiev, Yalchin; Galvis, Juan; Hou, Thomas Y. Journal of Computational Physics, Vol. 251 https://doi.org/10.1016/j.jcp.2013.04.045	journal	October 2013
Dynamically orthogonal field equations for continuous stochastic dynamical systems Sapsis, Themistoklis P.; Lermusiaux, Pierre F. J. Physica D: Nonlinear Phenomena, Vol. 238, Issue 23-24 https://doi.org/10.1016/j.physd.2009.09.017	journal	December 2009
A Stochastic Projection Method for Fluid Flow Le Maı̂ tre, Olivier P.; Knio, Omar M.; Najm, Habib N. Journal of Computational Physics, Vol. 173, Issue 2 https://doi.org/10.1006/jcph.2001.6889	journal	November 2001
Multi-Element Generalized Polynomial Chaos for Arbitrary Probability Measures Wan, Xiaoliang; Karniadakis, George Em SIAM Journal on Scientific Computing, Vol. 28, Issue 3 https://doi.org/10.1137/050627630	journal	January 2006
Proper Generalized Decompositions and Separated Representations for the Numerical Solution of High Dimensional Stochastic Problems Nouy, Anthony Archives of Computational Methods in Engineering, Vol. 17, Issue 4 https://doi.org/10.1007/s11831-010-9054-1	journal	October 2010
A generalized spectral decomposition technique to solve a class of linear stochastic partial differential equations Nouy, Anthony Computer Methods in Applied Mechanics and Engineering, Vol. 196, Issue 45-48 https://doi.org/10.1016/j.cma.2007.05.016	journal	September 2007
A fast randomized algorithm for the approximation of matrices Woolfe, Franco; Liberty, Edo; Rokhlin, Vladimir Applied and Computational Harmonic Analysis, Vol. 25, Issue 3 https://doi.org/10.1016/j.acha.2007.12.002	journal	November 2008
A Multiscale Data-Driven Stochastic Method for Elliptic PDEs with Random Coefficients Zhang, Zhiwen; Ci, Maolin; Hou, Thomas Y. Multiscale Modeling & Simulation, Vol. 13, Issue 1 https://doi.org/10.1137/130948136	journal	January 2015
A probabilistic graphical model approach to stochastic multiscale partial differential equations Wan, Jiang; Zabaras, Nicholas Journal of Computational Physics, Vol. 250 https://doi.org/10.1016/j.jcp.2013.05.016	journal	October 2013
A dynamically bi-orthogonal method for time-dependent stochastic partial differential equations I: Derivation and algorithms Cheng, Mulin; Hou, Thomas Y.; Zhang, Zhiwen Journal of Computational Physics, Vol. 242 https://doi.org/10.1016/j.jcp.2013.02.033	journal	June 2013
Galerkin Finite Element Approximations of Stochastic Elliptic Partial Differential Equations Babuska, Ivo; Tempone, Raúl; Zouraris, Georgios E. SIAM Journal on Numerical Analysis, Vol. 42, Issue 2 https://doi.org/10.1137/S0036142902418680	journal	January 2004

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