Generalized Multiscale Finite Element Methods for Wave Propagation in Heterogeneous Media [PDF]
Multiscale Modeling & Simulation, 2014 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.
Eric T. Chung +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
Eric T. Chung +2 more
core +7 more sources
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
Eric T. Chung +2 more
core +9 more sources
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.
Donald L. Brown, Maria Vasilyeva
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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).
Eric T. Chung +3 more
core +8 more sources
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 ...
Guanglian Li, Juan Galvis, Ke Shi
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Generalized Multiscale Finite Element Method for Elastic Wave Propagation in the Frequency Domain [PDF]
Computation, 2020 In this work, we consider elastic wave propagation in fractured media. The mathematical model is described by the Helmholtz problem related to wave propagation with specific interface conditions (Linear Slip Model, LSM) on the fracture in the frequency ...
Uygulana Gavrilieva +2 more
doaj +2 more sources
An Online Generalized Multiscale Finite Element Method for Unsaturated Filtration Problem in Fractured Media [PDF]
Mathematics, 2021 In this paper, we present a multiscale model reduction technique for unsaturated filtration problem in fractured porous media using an Online Generalized Multiscale finite element method. The flow problem in unsaturated soils is described by the Richards
Denis Spiridonov +3 more
doaj +2 more sources
GENERALIZED MULTISCALE FINITE ELEMENT METHODS: OVERSAMPLING STRATEGIES [PDF]
International Journal for Multiscale Computational Engineering, 2014 In this paper, we propose oversampling strategies in the Generalized Multiscale Finite Element Method (GMsFEM) framework. The GMsFEM, which has been recently introduced in [12], allows solving multiscale parameter-dependent problems at a reduced computational cost by constructing a reduced-order representation of the solution on a coarse grid. The main
Yalchin Efendiev +3 more
openalex +5 more sources
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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