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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.
Chung, Eric +2 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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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.
Chung, Eric T. +2 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 ...
Efendiev, Yalchin +2 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, Juan, Li, Guanglian, Shi, Ke
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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 Methods for Wave Propagation in Heterogeneous Media [PDF]
Multiscale Modeling & Simulation, 2014 Numerical modeling of wave propagation in heterogeneous media is important in many applications. Due to the complex nature, direct numerical simulations on the fine grid are prohibitively expensive. It is therefore important to develop efficient and accurate methods that allow the use of coarse grids.
Chung, Eric T. +2 more
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Fast online generalized multiscale finite element method using constraint energy minimization [PDF]
Journal of Computational Physics, 2018 Local multiscale methods often construct multiscale basis functions in the offline stage without taking into account input parameters, such as source terms, boundary conditions, and so on. These basis functions are then used in the online stage with a specific input parameter to solve the global problem at a reduced computational cost. Recently, online
Chung, Eric T. +2 more
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Generalized multiscale finite element methods for problems in perforated heterogeneous domains [PDF]
Applicable Analysis, 2015 Complex processes in perforated domains occur in many real-world applications. These problems are typically characterized by physical processes in domains with multiple scales (see Figure 1 for the illustration of a perforated domain). Moreover, these problems are intrinsically multiscale and their discretizations can yield very large linear or ...
Chung, Eric T. +3 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 ...
Brown, Donald, Vasilyeva, Maria
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