Results 11 to 20 of about 1,889 (249)
Randomized Oversampling for Generalized Multiscale Finite Element Methods [PDF]
Multiscale Modeling & Simulation, 2016 In this paper, we study the development of efficient multiscale methods for flows in heterogeneous media. Our approach uses the Generalized Multiscale Finite Element (GMsFEM) framework. The main idea of GMsFEM is to approximate the solution space locally using a few multiscale basis functions.
Victor M. Calo +3 more
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Mixed Generalized Multiscale Finite Element Method for a Simplified Magnetohydrodynamics Problem in Perforated Domains [PDF]
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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Generalized multiscale finite element methods (GMsFEM) [PDF]
Journal of Computational Physics, 2013 In this paper, we propose a general approach called Generalized Multiscale Finite Element Method (GMsFEM) for performing multiscale simulations for problems without scale separation over a complex input space. As in multiscale finite element methods (MsFEMs), the main idea of the proposed approach is to construct a small dimensional local solution ...
Yalchin Efendiev +2 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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Mixed Generalized Multiscale Finite Element Methods and Applications [PDF]
Multiscale Modeling & Simulation, 2015 In this paper, we present a mixed Generalized Multiscale Finite Element Method (GMsFEM) for solving flow in heterogeneous media. Our approach constructs multiscale basis functions following a GMsFEM framework and couples these basis functions using a mixed finite element method, which allows us to obtain a mass conservative velocity field. To construct
Eric T. Chung 0001 +2 more
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Sparse Generalized Multiscale Finite Element Methods and their applications [PDF]
International Journal for Multiscale Computational Engineering, 2015 In a number of previous papers, local (coarse grid) multiscale model reduction techniques are developed using a Generalized Multiscale Finite Element Method. In these approaches, multiscale basis functions are constructed using local snapshot spaces, where a snapshot space is a large space that represents the solution behavior in a coarse block.
Chung, Eric T. +3 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 be highly heterogeneous and have high contrast. We present the construction of main ingredients for
Chung, Eric T. +2 more
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An exponential integration generalized multiscale finite element method for parabolic problems [PDF]
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
Contreras, L.F. +5 more
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A generalized multiscale finite element method for poroelasticity problems II: Nonlinear coupling [PDF]
Journal of Computational and Applied Mathematics, 2016 arXiv admin note: text overlap with arXiv:1304.5188 by other ...
Donald L. Brown, Maria V. Vasilyeva
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Generalized Multiscale Finite Element Methods. Nonlinear Elliptic Equations [PDF]
Communications in Computational Physics, 2014 In this paper we use the GeneralizedMultiscale Finite ElementMethod (GMsFEM) framework, introduced in [20], 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 parameters ...
Efendiev, Yalchin R. +3 more
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