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Generalized Multiscale Finite Element Method for Elastic Wave Propagation in the Frequency Domain
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 Efendiev et al. (2013b) [Generalized Multiscale Finite Element Methods, J. Comput.
Presho, Michael +4 more
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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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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
Journal of Computational and Applied Mathematics, 2015 © 2014 Elsevier B.V. All rights reserved. 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
Guanglian Li +5 more
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Computation, 2020 In this paper, we consider a coupled system of equations that describes simplified magnetohydrodynamics (MHD) problem in perforated domains. We construct a fine grid that resolves the perforations on the grid level in order to use a traditional ...
Valentin Alekseev +4 more
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Mixed Generalized Multiscale Finite Element Method for Darcy-Forchheimer Model
Mathematics, 2019 In this paper, the solution of the Darcy-Forchheimer model in high contrast heterogeneous media is studied. This problem is solved by a mixed finite element method (MFEM) on a fine grid (the reference solution), where the pressure is approximated by ...
Denis Spiridonov +4 more
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Journal of Computational Physics, 2018 We propose a generalized multiscale finite element method (GMsFEM) based on clustering algorithm to study the elliptic PDEs with random coefficients in the multi-query setting. Our method consists of offline and online stages.
Wing Tat Leung +7 more
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Journal of Computational Physics, 2015 It is important to develop fast yet accurate numerical methods for seismic wave propagation to characterize complex geological structures and oil and gas reservoirs.
Shubin Fu +9 more
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