Constraint energy minimizing generalized multiscale finite element method for multi-continuum Richards equations [PDF]
Journal of Computational Physics, 2023 Tina 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
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An exponential integration generalized multiscale finite element method for parabolic problems
Journal of Computational Physics, 2023 We consider linear and semilinear parabolic problems posed in high-contrast multiscale media in two dimensions. The presence of high-contrast multiscale media adversely affects the accuracy, stability, and overall efficiency of numerical approximations such as finite elements in space combined with some time integrator. In many cases, implementing time
L.F. Contreras +5 more
semanticscholar +3 more sources
Nonconforming generalized multiscale finite element methods
Journal of Computational and Applied Mathematics, 2016 A framework is introduced for nonconforming multiscale approach based on GMsFEM (Generalized Multiscale Finite Element Method). Snapshot spaces are constructed for each macro-scale block. The snapshot spaces can be based on either conforming or nonconforming elements. With suitable dimension reduction, offline spaces are constructed.
Chak Shing Lee, Dongwoo Sheen
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Constraint energy minimizing generalized multiscale finite element method for nonlinear poroelasticity and elasticity [PDF]
Journal of Computational Physics, 2020 Shubin Fu, Eric T. Chung, Tina Mai
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Generalized Multiscale Finite Element Method for the Steady State Linear Boltzmann Equation [PDF]
Multiscale Modeling & Simulation, 2020 The Boltzmann equation, as a model equation in statistical mechanics, is used to describe the statistical behavior of a large number of particles driven by the same physics laws. Depending on the media and the particles to be modeled, the equation has slightly different forms.
Eric T. Chung +3 more
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Generalized multiscale finite element method. Symmetric interior penalty coupling [PDF]
Journal of Computational Physics, 2013 Motivated by applications to numerical simulation of flows in highly heterogeneous porous media, we develop multiscale finite element methods for second order elliptic equations. We discuss a multiscale model reduction technique in the framework of the discontinuous Galerkin finite element method. We propose three different finite element spaces on the
Yalchin Efendiev +4 more
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Constraint energy minimizing generalized multiscale finite element method for inhomogeneous boundary value problems with high contrast coefficients [PDF]
Multiscale Modeling & simulation, 2022 In this article we develop the Constraint Energy Minimizing Generalized Multiscale Finite Element Method (CEM-GMsFEM) for elliptic partial differential equations with inhomogeneous Dirichlet, Neumann, and Robin boundary conditions, and the high contrast ...
Changqing Ye, Eric T. Chung
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An Online Generalized Multiscale finite element method for heat and mass transfer problem with artificial ground freezing [PDF]
Journal of Computational and Applied Mathematics, 2022 In this paper, we present an Online Generalized Multiscale Finite Element Method(Online GMsFEM) for heat and mass transfer problem in heterogeneous media with artificial ground freezing pipes.
D. Spiridonov, S. Stepanov, V. Vasiliy
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Generalized Multiscale Finite Element Method for the poroelasticity problem in multicontinuum media [PDF]
Journal of Computational and Applied Mathematics, 2020 In this paper, we consider a poroelasticity problem in heterogeneous multicontinuum media that is widely used in simulations of the unconventional hydrocarbon reservoirs and geothermal fields. Mathematical model contains a coupled system of equations for pressures in each continuum and effective equation for displacement with volume force sources that ...
Aleksei Tyrylgin +3 more
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