skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

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

Authors:
; ; ; ORCiD logo
Publication Date:
Sponsoring Org.:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
OSTI Identifier:
1564505
Grant/Contract Number:  
FG02-13ER26165; SC0010713
Resource Type:
Publisher's Accepted Manuscript
Journal Name:
Journal of Computational Physics
Additional Journal Information:
Journal Name: Journal of Computational Physics Journal Volume: 371 Journal Issue: C; Journal ID: ISSN 0021-9991
Publisher:
Elsevier
Country of Publication:
United States
Language:
English

Citation Formats

Chung, Eric T., Efendiev, Yalchin, Leung, Wing Tat, and Zhang, Zhiwen. Cluster-based generalized multiscale finite element method for elliptic PDEs with random coefficients. United States: N. p., 2018. Web. https://doi.org/10.1016/j.jcp.2018.05.041.
Chung, Eric T., Efendiev, Yalchin, Leung, Wing Tat, & Zhang, Zhiwen. Cluster-based generalized multiscale finite element method for elliptic PDEs with random coefficients. United States. https://doi.org/10.1016/j.jcp.2018.05.041
Chung, Eric T., Efendiev, Yalchin, Leung, Wing Tat, and Zhang, Zhiwen. Mon . "Cluster-based generalized multiscale finite element method for elliptic PDEs with random coefficients". United States. https://doi.org/10.1016/j.jcp.2018.05.041.
@article{osti_1564505,
title = {Cluster-based generalized multiscale finite element method for elliptic PDEs with random coefficients},
author = {Chung, Eric T. and Efendiev, Yalchin and Leung, Wing Tat and Zhang, Zhiwen},
abstractNote = {},
doi = {10.1016/j.jcp.2018.05.041},
journal = {Journal of Computational Physics},
number = C,
volume = 371,
place = {United States},
year = {2018},
month = {10}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
https://doi.org/10.1016/j.jcp.2018.05.041

Citation Metrics:
Cited by: 2 works
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

Uncertainty Quantification and Polynomial Chaos Techniques in Computational Fluid Dynamics
journal, January 2009


Finding Structure with Randomness: Probabilistic Algorithms for Constructing Approximate Matrix Decompositions
journal, January 2011

  • Halko, N.; Martinsson, P. G.; Tropp, J. A.
  • SIAM Review, Vol. 53, Issue 2
  • DOI: 10.1137/090771806

Residual-driven online generalized multiscale finite element methods
journal, December 2015

  • Chung, Eric T.; Efendiev, Yalchin; Leung, Wing Tat
  • Journal of Computational Physics, Vol. 302
  • DOI: 10.1016/j.jcp.2015.07.068

Randomized algorithms for the low-rank approximation of matrices
journal, December 2007

  • Liberty, E.; Woolfe, F.; Martinsson, P. -G.
  • Proceedings of the National Academy of Sciences, Vol. 104, Issue 51
  • DOI: 10.1073/pnas.0709640104

Modeling uncertainty in flow simulations via generalized polynomial chaos
journal, May 2003


A Multiscale Finite Element Method for Elliptic Problems in Composite Materials and Porous Media
journal, June 1997

  • Hou, Thomas Y.; Wu, Xiao-Hui
  • Journal of Computational Physics, Vol. 134, Issue 1
  • DOI: 10.1006/jcph.1997.5682

An adaptive GMsFEM for high-contrast flow problems
journal, September 2014


Adaptive multiscale model reduction with Generalized Multiscale Finite Element Methods
journal, September 2016


Convergence of a Nonconforming Multiscale Finite Element Method
journal, January 2000

  • Efendiev, Yalchin R.; Hou, Thomas Y.; Wu, Xiao-Hui
  • SIAM Journal on Numerical Analysis, Vol. 37, Issue 3
  • DOI: 10.1137/S0036142997330329

Monte Carlo and quasi-Monte Carlo methods
journal, January 1998


Randomized Oversampling for Generalized Multiscale Finite Element Methods
journal, January 2016

  • Calo, Victor M.; Efendiev, Yalchin; Galvis, Juan
  • Multiscale Modeling & Simulation, Vol. 14, Issue 1
  • DOI: 10.1137/140988826

Multilevel Monte Carlo Path Simulation
journal, June 2008


Generalized multiscale finite element methods (GMsFEM)
journal, October 2013


A Stochastic Projection Method for Fluid Flow
journal, November 2001

  • Le Maı̂ tre, Olivier P.; Knio, Omar M.; Najm, Habib N.
  • Journal of Computational Physics, Vol. 173, Issue 2
  • DOI: 10.1006/jcph.2001.6889

Multi-Element Generalized Polynomial Chaos for Arbitrary Probability Measures
journal, January 2006

  • Wan, Xiaoliang; Karniadakis, George Em
  • SIAM Journal on Scientific Computing, Vol. 28, Issue 3
  • DOI: 10.1137/050627630

Proper Generalized Decompositions and Separated Representations for the Numerical Solution of High Dimensional Stochastic Problems
journal, October 2010


A fast randomized algorithm for the approximation of matrices
journal, November 2008

  • Woolfe, Franco; Liberty, Edo; Rokhlin, Vladimir
  • Applied and Computational Harmonic Analysis, Vol. 25, Issue 3
  • DOI: 10.1016/j.acha.2007.12.002

A Multiscale Data-Driven Stochastic Method for Elliptic PDEs with Random Coefficients
journal, January 2015

  • Zhang, Zhiwen; Ci, Maolin; Hou, Thomas Y.
  • Multiscale Modeling & Simulation, Vol. 13, Issue 1
  • DOI: 10.1137/130948136

A probabilistic graphical model approach to stochastic multiscale partial differential equations
journal, October 2013


Galerkin Finite Element Approximations of Stochastic Elliptic Partial Differential Equations
journal, January 2004

  • Babuska, Ivo; Tempone, Raúl; Zouraris, Georgios E.
  • SIAM Journal on Numerical Analysis, Vol. 42, Issue 2
  • DOI: 10.1137/S0036142902418680