, 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.
Eric T. Chung +3 more
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Constraint energy minimizing generalized multiscale finite element method for convection diffusion equation [PDF]
Multiscale Modeling & simulation, 2022 In this paper we present and analyze a constraint energy minimizing generalized multiscale finite element method for convection diffusion equation. To define the multiscale basis functions, we first build an auxiliary multiscale space by solving local ...
Lina Zhao, Eric T. Chung
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A mixed multiscale spectral generalized finite element method [PDF]
Numerische MathematikWe present a multiscale mixed finite element method for solving second order elliptic equations with general $L^{\infty}$-coefficients arising from flow in highly heterogeneous porous media.
Christian Alber +2 more
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Generalized Multiscale Finite Element Methods for Wave Propagation in Heterogeneous Media [PDF]
, 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.
Eric T. Chung +2 more
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Constraint energy minimizing generalized multiscale finite element method for dual continuum model [PDF]
Communications in Mathematical Sciences, 2020 The dual continuum model serves as a powerful tool in the modeling of subsurface applications. It allows a systematic coupling of various components of the solutions.
Siu Wun Cheung +4 more
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A Generalized Multiscale Finite Element Method for poroelasticity problems I: Linear problems [PDF]
, 2015 In this paper, we consider the numerical solution of poroelasticity problems that are of Biot type and develop a general algorithm for solving coupled systems.
Donald L. Brown, Maria Vasilyeva
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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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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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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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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 ...
Yalchin Efendiev +4 more
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