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
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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
Galvis J +2 more
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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
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Multiscale Simulations for Coupled Flow and Transport Using the Generalized Multiscale Finite Element Method [PDF]
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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A generalized multiscale finite element method for the Brinkman equation [PDF]
Journal of Computational and Applied Mathematics, 2015 22 ...
Galvis J, Ke Shi, Guanglian Li
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Generalized Multiscale Finite Element Method and Balanced Truncation for Parameter-Dependent Parabolic Problems [PDF]
Mathematics, 2023 We propose a generalized multiscale finite element method combined with a balanced truncation to solve a parameter-dependent parabolic problem. As an updated version of the standard multiscale method, the generalized multiscale method contains the ...
Shan Jiang +3 more
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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 intended to be comprehensive.
Yalchin Efendiev +2 more
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Constraint Energy Minimizing Generalized Multiscale Finite Element Method [PDF]
Computer Methods in Applied Mechanics and Engineering, 2018 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. We would like to show a mesh-dependent convergence with a minimal number of basis functions.
Yalchin Efendiev +2 more
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Mixed Generalized Multiscale Finite Element Method for flow problem in thin domains
Journal of Computational and Applied Mathematics, 2022 In this paper, we construct a class of Mixed Generalized Multiscale Finite Element Methods for the approximation on a coarse grid for an elliptic problem in thin two-dimensional domains. We consider the elliptic equation with homogeneous boundary conditions on the domain walls. For reference solution of the problem, we use a Mixed Finite Element Method
Maria Vasilyeva +2 more
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Application of a conservative, generalized multiscale finite element method to flow models
Journal of Computational and Applied Mathematics, 2014 27 pages, 10 ...
VĂCTOR Ginting, Michael Presho
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