Prediction of Discretization of GMsFEM Using Deep Learning [PDF]
Mathematics, 2019 In this paper, we propose a deep-learning-based approach to a class of multiscale problems. The generalized multiscale finite element method (GMsFEM) has been proven successful as a model reduction technique of flow problems in heterogeneous and high ...
Min Wang, Siu Wun Cheung, Eric Chung
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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.
Yalchin Efendiev, Juan Galvis
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DG-GMsFEM for Problems in Perforated Domains with Non-Homogeneous Boundary Conditions [PDF]
Computation, 2021 Problems in perforated media are complex and require high resolution grid construction to capture complex irregular perforation boundaries leading to the large discrete system of equations. In this paper, we develop a multiscale model reduction technique
Maria Vasilyeva +2 more
exaly +4 more sources
An adaptive GMsFEM for high-contrast flow problems [PDF]
Journal of Computational Physics, 2013 In this paper, we derive an a-posteriori error indicator for the Generalized Multiscale Finite Element Method (GMsFEM) framework. This error indicator is further used to develop an adaptive enrichment algorithm for the linear elliptic equation with ...
Chung, Eric T. +2 more
core +3 more sources
Adaptive Multiscale Model Reduction for Nonlinear Parabolic Equations Using GMsFEM [PDF]
Computational Science – ICCS 2020, 2020 14 pages.
Wang, Yiran, Chung, Eric, Fu, Shubin
openaire +3 more sources
Numerical Study of Soil-Thawing Effect of Composite Piles Using GMsFEM [PDF]
Journal of Composites Science, 2021 During construction works, it is advisable to prevent strong thawing and an increase in the moisture content of the foundations of engineering structures in the summer. Since the density of water and ice differ, due to the difference bulging of the foundation sections can occur when it freezes back in winter.
Petr V Sivtsev, Piotr Smarzewski
exaly +2 more sources
Mixed GMsFEM for linear poroelasticity problems in heterogeneous porous media [PDF]
Journal of Computational and Applied Mathematics, 2021 Accurate numerical simulations of interaction between fluid and solid play an important role in applications. The task is challenging in practical scenarios as the media are usually highly heterogeneous with very large contrast. To overcome this computational challenge, various multiscale methods are developed.
Xia Wang, Eric Chung, Shubin Fu
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Computational multiscale methods for first-order wave equation using mixed CEM-GMsFEM [PDF]
Journal of Computational Physics, 2020 In this paper, we consider a pressure-velocity formulation of the heterogeneous wave equation and employ the constraint energy minimizing generalized multiscale finite element method (CEM-GMsFEM) to solve this problem. The proposed method provides a flexible framework to construct crucial multiscale basis functions for approximating the pressure and ...
Eric Chung, Sai-Mang Pun
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Convergence of the CEM-GMsFEM for Stokes flows in heterogeneous perforated domains [PDF]
Journal of Computational and Applied Mathematics, 2021 18 pages, 2 ...
Eric Chung, Jiuhua Hu, Sai-Mang Pun
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Generalized Multiscale Finite-Element Method (GMsFEM) for elastic wave propagation in heterogeneous, anisotropic media [PDF]
Journal of Computational Physics, 2015 It is important to develop fast yet accurate numerical methods for seismic wave propagation to characterize complex geological structures and oil and gas reservoirs. However, the computational cost of conventional numerical modeling methods, such as finite-difference method and finite-element method, becomes prohibitively expensive when applied to very
Kai Gao, Shubin Fu, Richard L Gibson
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