Generalized Multiscale Finite Element Method for discrete network (graph) models [PDF]
Journal of Computational and Applied MathematicsIn this paper, we consider a time-dependent discrete network model with highly varying connectivity. The approximation by time is performed using an implicit scheme.
Maria Vasilyeva
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Hierarchical multiscale modeling for flows in fractured media using generalized multiscale finite element method [PDF]
GEM - International Journal on Geomathematics, 2015 In this paper, we develop a multiscale finite element method for solving flows in fractured media. Our approach is based on generalized multiscale finite element method (GMsFEM), where we represent the fracture effects on a coarse grid via multiscale ...
Y. Efendiev +4 more
semanticscholar +8 more sources
A Constraint Energy Minimizing Generalized Multiscale Finite Element Method for Parabolic Equations [PDF]
Multiscale Modeling & Simulation, 2018 In this paper, we present a Constraint Energy Minimizing Generalized Multiscale Finite Element Method (CEM-GMsFEM) for parabolic equations with multiscale coefficients, arising from applications in porous media.
Mengnan Li, Eric T. Chung, Lijian Jiang
semanticscholar +7 more sources
Mixed Generalized Multiscale Finite Element Method for Darcy-Forchheimer Model [PDF]
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 ...
D. Spiridonov +4 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. We would like to show a mesh-dependent convergence with a minimal number of basis functions.
Eric T. Chung, Y. Efendiev, W. Leung
semanticscholar +6 more sources
Generalized multiscale finite element method for a nonlinear elastic strain-limiting Cosserat model [PDF]
Journal of Computational PhysicsFor nonlinear Cosserat elasticity, we consider multiscale methods in this paper. In particular, we explore the generalized multiscale finite element method (GMsFEM) to solve an isotropic Cosserat problem with strain-limiting property (ensuring bounded ...
Dmitry Ammosov, Tina Mai, Juan Galvis
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An iterative constraint energy minimizing generalized multiscale finite element method for contact problem [PDF]
Journal of Computational and Applied MathematicsThis work presents an Iterative Constraint Energy Minimizing Generalized Multiscale Finite Element Method (ICEM-GMsFEM) for solving the contact problem with high contrast coefficients.
Zishang Li, Changqing Ye, Eric T. Chung
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Journal of Physics: Conference Series, 2019 In this work, we consider a pororelasticity problem in fractured porous media. Mathematical model contains a coupled system of equations for pressure and displacements, for which we use an embedded fracture model.
A. Tyrylgin, M. Vasilyeva, Eric T. Chung
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Constraint Energy Minimizing Generalized Multiscale Finite Element Method for multi-continuum Richards equations [PDF]
Journal of Computational Physics, 2022 T. Mai +2 more
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Generalized Multiscale Finite Element Methods. Nonlinear Elliptic Equations [PDF]
Communications in Computational Physics, 2013 AbstractIn this paper we use the Generalized Multiscale Finite Element Method (GMsFEM) framework, introduced in [26], in order to solve nonlinear elliptic equations with high-contrast coefficients. The proposed solution method involves linearizing the equation so that coarse-grid quantities of previous solution iterates can be regarded as auxiliary ...
Yalchin Efendiev +3 more
openalex +6 more sources