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A multiscale finite element method for soil-rock mixture
Frontiers in Materials, 2023 Soil-rock mixture is a complex multi-phase composite geotechnical material, and its strength is determined by the physical properties of constituent multi-phase materials and their coupling mechanical response between different phases of materials. Based
Jia Liu, Deluan Feng
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Exponentially Convergent Multiscale Finite Element Method
Communications on Applied Mathematics and Computation, 2023 We provide a concise review of the exponentially convergent multiscale finite element method (ExpMsFEM) for efficient model reduction of PDEs in heterogeneous media without scale separation and in high-frequency wave propagation. ExpMsFEM is built on the non-overlapped domain decomposition in the classical MsFEM while enriching the approximation space ...
Yifan Chen, Thomas Y. Hou, Yixuan Wang
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High-Speed Railway, 2023 In order to make further study on the mechanical property of CRTSIII type slab non-ballast track structures, which was self-designed in China, based on the method of the multiscale finite element model (FEM), the traditional FEM of slab non-ballast track
Yuhang Wang +4 more
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Mathematics, 2023 We propose a generalized multiscale finite element method combined with a balanced truncation to solve a parameter-dependent parabolic problem. As an updated version of the standard multiscale method, the generalized multiscale method contains the ...
Shan Jiang +3 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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An Adaptive Multiscale Finite Element Method [PDF]
Multiscale Modeling & Simulation, 2014 This work is devoted to an adaptive multiscale finite element method (MsFEM) for solving elliptic problems with rapidly oscillating coeefficients. Starting from a general version of the MsFEM with oversampling, we de- rive an a posteriori estimate for the H1-error between the exact solution of the problem and a corresponding MsFEM approximation.
Henning, Patrick +2 more
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Generalized Multiscale Finite Element Method for Elastic Wave Propagation in the Frequency Domain
Computation, 2020 In this work, we consider elastic wave propagation in fractured media. The mathematical model is described by the Helmholtz problem related to wave propagation with specific interface conditions (Linear Slip Model, LSM) on the fracture in the frequency ...
Uygulana Gavrilieva +2 more
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Mathematics, 2021 In this paper, we present a multiscale model reduction technique for unsaturated filtration problem in fractured porous media using an Online Generalized Multiscale finite element method. The flow problem in unsaturated soils is described by the Richards
Denis Spiridonov +3 more
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GENERALIZED MULTISCALE FINITE ELEMENT METHODS: OVERSAMPLING STRATEGIES [PDF]
International Journal for Multiscale Computational Engineering, 2014 In this paper, we propose oversampling strategies in the Generalized Multiscale Finite Element Method (GMsFEM) framework. The GMsFEM, which has been recently introduced in [12], allows solving multiscale parameter-dependent problems at a reduced computational cost by constructing a reduced-order representation of the solution on a coarse grid. The main
Efendiev, Yalchin R. +3 more
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Oversampling for the Multiscale Finite Element Method [PDF]
Multiscale Modeling & Simulation, 2013 This paper reviews standard oversampling strategies as performed in the Multiscale Finite Element Method (MsFEM). Common to those approaches is that the oversampling is performed in the full space restricted to a patch but including coarse finite element functions.
Henning, Patrick, Peterseim, Daniel
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