Generalized Multiscale Finite Element Methods for problems in perforated heterogeneous domains [PDF]
, 2015 Complex processes in perforated domains occur in many real-world applications. These problems are typically characterized by physical processes in domains with multiple scales (see Figure 1 for the illustration of a perforated domain).
Chung, Eric T. +3 more
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Computation, 2015 In this paper, we develop a mass conservative multiscale method for coupled flow and transport in heterogeneous porous media. We consider a coupled system consisting of a convection-dominated transport equation and a flow equation.
Eric T. Chung +3 more
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Computational Multiscale Methods for Linear Poroelasticity with High Contrast [PDF]
, 2018 In this work, we employ the Constraint Energy Minimizing Generalized Multiscale Finite Element Method (CEM-GMsFEM) to solve the problem of linear heterogeneous poroelasticity with coefficients of high contrast.
Altmann, Robert +5 more
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Goal-oriented adaptivity for GMsFEM
Journal of Computational and Applied Mathematics, 2016 16 pages, 4 ...
Eric T. Chung +2 more
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Generalized multiscale finite element methods for wave propagation in heterogeneous media [PDF]
, 2013 Numerical modeling of wave propagation in heterogeneous media is important in many applications. Due to the complex nature, direct numerical simulations on the fine grid are prohibitively expensive.
Chung, Eric T. +2 more
core +3 more sources
Expanded mixed multiscale finite element methods and their applications for flows in porous media [PDF]
, 2012 We develop a family of expanded mixed Multiscale Finite Element Methods (MsFEMs) and their hybridizations for second-order elliptic equations. This formulation expands the standard mixed Multiscale Finite Element formulation in the sense that four ...
Arnold D. N. +4 more
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A Generalized Multiscale Finite Element Method for Poroelasticity Problems I: Linear Problems [PDF]
, 2015 In this paper, we consider the numerical solution of poroelasticity problems that are of Biot type and develop a general algorithm for solving coupled systems.
Brown, Donald L., Vasilyeva, Maria
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Convergence analysis for GMsFEM approximation of elliptic eigenvalue problems
Journal of Computational and Applied Mathematics, 2018 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ma, Lingling, Jiang, Lijian
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A Hybrid Model Reduction Method for Dual-Continuum Model with Random Inputs
ComputationIn this paper, a hybrid model reduction method for solving flows in fractured media is proposed. The approach integrates the Generalized Multiscale Finite Element Method (GMsFEM) with a novel variable-separation (VS) technique.
Lingling Ma
doaj +1 more source
Nonlinear nonlocal multicontinua upscaling framework and its applications
, 2018 In this paper, we discuss multiscale methods for nonlinear problems. The main idea of these approaches is to use local constraints and solve problems in oversampled regions for constructing macroscopic equations.
Chung, Eric T. +3 more
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