Adaptive multiscale model reduction with Generalized Multiscale Finite Element Methods [PDF]
Journal of Computational Physics, 2016 In this paper, we discuss a general multiscale model reduction framework based on multiscale finite element methods. We give a brief overview of related multiscale methods. Due to page limitations, the overview focuses on a few related methods and is not
Chung, Eric +2 more
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Generalized Multiscale Finite Element Method for Elasticity Equations [PDF]
GEM - International Journal on Geomathematics, 2014 In this paper, we discuss the application of Generalized Multiscale Finite Element Method (GMsFEM) to elasticity equation in heterogeneous media. Our applications are motivated by elastic wave propagation in subsurface where the subsurface properties can
Chung, Eric T. +2 more
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Constraint Energy Minimizing Generalized Multiscale Finite Element Method [PDF]
Computer Methods in Applied Mechanics and Engineering, 2017 The main goal of this paper is to design multiscale basis functions within GMsFEM framework such that the convergence of method is independent of the contrast and linearly decreases with respect to mesh size if oversampling size is appropriately chosen ...
Chung, Eric T. +2 more
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A Generalized Multiscale Finite Element Method for the Brinkman Equation [PDF]
Journal of Computational and Applied Mathematics, 2014 In this paper we consider the numerical upscaling of the Brinkman equation in the presence of high-contrast permeability fields. We develop and analyze a robust and efficient Generalized Multiscale Finite Element Method (GMsFEM) for the Brinkman model ...
Galvis, Juan, Li, Guanglian, Shi, Ke
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Fast Online Generalized Multiscale Finite Element Method using Constraint Energy Minimization [PDF]
Journal of Computational Physics, 2017 Local multiscale methods often construct multiscale basis functions in the offline stage without taking into account input parameters, such as source terms, boundary conditions, and so on.
Chung, Eric T. +2 more
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Generalized multiscale finite element methods for wave propagation in heterogeneous media [PDF]
Multiscale Modeling & Simulation, 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
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Generalized Multiscale Finite Element Methods for problems in perforated heterogeneous domains [PDF]
Applicable Analysis, 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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Sparse Generalized Multiscale Finite Element Methods and their applications [PDF]
International Journal for Multiscale Computational Engineering, 2015 In a number of previous papers, local (coarse grid) multiscale model reduction techniques are developed using a Generalized Multiscale Finite Element Method.
Chung, Eric +3 more
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A Generalized Multiscale Finite Element Method for Poroelasticity Problems I: Linear Problems [PDF]
Journal of Computational and Applied Mathematics, 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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A Generalized Multiscale Finite Element Method for poroelasticity problems II: nonlinear coupling [PDF]
Journal of Computational and Applied Mathematics, 2015 In this paper, we consider the numerical solution of some nonlinear poroelasticity problems that are of Biot type and develop a general algorithm for solving nonlinear coupled systems.
Abdulle +18 more
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