Constraint Energy Minimizing Generalized Multiscale Finite Element Method
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In this article, the authors proposed a constraint energy minimization to construct multiscale spaces for GMsFEM, which is performed in the oversampling domain, which can handle non-decaying components of the local minimizers.About:
This article is published in Computer Methods in Applied Mechanics and Engineering.The article was published on 2018-09-01 and is currently open access. It has received 151 citations till now. The article focuses on the topics: Basis function & Basis (linear algebra).read more
Citations
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Journal ArticleDOI
Non-local Multi-continua Upscaling for Flows in Heterogeneous Fractured Media
Eric T. Chung,Yalchin Efendiev,Wing Tat Leung,Maria V. Vasilyeva,Maria V. Vasilyeva,Yating Wang +5 more
TL;DR: A rigorous and accurate non-local (in the oversampled region) upscaling framework based on some recently developed multiscale methods is proposed based on Generalized Multiscale Finite Element Method (GMsFEM) and can provide good accuracy.
Journal ArticleDOI
Multiscale model reduction for shale gas transport in poroelastic fractured media
TL;DR: A multiscale model reduction approach to couple gas flow and geomechanics in fractured shale media and a coarse grid approximation and coupling using the Generalized Multiscale Finite Element Method (GMsFEM).
Journal ArticleDOI
Constraint energy minimizing generalized multiscale finite element method for nonlinear poroelasticity and elasticity
Shubin Fu,Eric T. Chung,Tina Mai +2 more
TL;DR: 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.
Journal ArticleDOI
Deep multiscale model learning
Yating Wang,Yating Wang,Siu Wun Cheung,Eric T. Chung,Yalchin Efendiev,Yalchin Efendiev,Min Wang,Min Wang +7 more
TL;DR: In this paper, a multi-layer neural network is proposed for multiscale simulations of flows taking into account the observed fine data and physical modeling concepts to predict flow dynamics in porous media.
Journal ArticleDOI
Constrained energy minimization based upscaling for coupled flow and mechanics
TL;DR: An embedded fracture model (EFM) for coupled flow and mechanics problem based on the dual continuum approach on the fine grid and an upscaled model for the resulting fine grid equations are presented.
References
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Journal ArticleDOI
A Multiscale Finite Element Method for Elliptic Problems in Composite Materials and Porous Media
Thomas Y. Hou,Xiao-Hui Wu +1 more
TL;DR: This paper studies a multiscale finite element method for solving a class of elliptic problems arising from composite materials and flows in porous media, which contain many spatial scales and proposes an oversampling technique to remove the resonance effect.
Journal ArticleDOI
Multiscale phenomena: Green's functions, the Dirichlet-to-Neumann formulation, subgrid scale models, bubbles and the origins of stabilized methods
TL;DR: In this paper, an approach is developed for deriving variational methods capable of representing multiscale phenomena, which leads to the well-known Dirichlet-to-Neumann formulation.
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The variational multiscale method—a paradigm for computational mechanics
TL;DR: In this article, a general treatment of the variational multiscale method in the context of an abstract Dirichlet problem is presented, showing how the exact theory represents a paradigm for subgrid-scale models and a posteriori error estimation.
Journal ArticleDOI
Variational multiscale residual-based turbulence modeling for large eddy simulation of incompressible flows
Yuri Bazilevs,Victor M. Calo,J. A. Cottrell,Thomas J. R. Hughes,Alessandro Reali,Guglielmo Scovazzi +5 more
TL;DR: In this paper, an LES-type variational multiscale theory of turbulence is presented, which derives completely from the incompressible Navier-Stokes equations and does not employ any ad hoc devices such as eddy viscosities.
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Equation-Free, Coarse-Grained Multiscale Computation: Enabling Mocroscopic Simulators to Perform System-Level Analysis
C. William Gear,James M. Hyman,Panagiotis G Kevrekidid,Ioannis G. Kevrekidis,Olof Runborg,Constantinos Theodoropoulos +5 more
TL;DR: A framework for computer-aided multiscale analysis, which enables models at a fine (microscopic/stochastic) level of description to perform modeling tasks at a coarse (macroscopic, systems) level, and can bypass the derivation of the macroscopic evolution equations when these equations conceptually exist but are not available in closed form is presented.
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