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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
Chung, Eric +2 more
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Convergence of a nonconforming multiscale finite element method [PDF]
SIAM Journal on Numerical Analysis, 2000 The multiscale finite element method (MsFEM) [T. Y. Hou, X. H. Wu, and Z. Cai, Math. Comp., 1998, to appear; T. Y. Hou and X. H. Wu, J. Comput. Phys., 134 (1997), pp. 169-189] has been introduced to capture the large scale solutions of elliptic equations
Efendiev, Yalchin R. +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
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, 2017 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 ...
Chung, Eric T. +2 more
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Generalized multiscale finite element method. Symmetric interior penalty coupling [PDF]
Journal of Computational Physics, 2013 Motivated by applications to numerical simulation of flows in highly heterogeneous porous media, we develop multiscale finite element methods for second order elliptic equations. We discuss a multiscale model reduction technique in the framework of the discontinuous Galerkin finite element method. We propose three different finite element spaces on the
Efendiev, Yalchin R. +4 more
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A Multiscale Mortar Mixed Finite Element Method [PDF]
Multiscale Modeling & Simulation, 2007 We develop multiscale mortar mixed finite element discretizations for second order elliptic equations. The continuity of flux is imposed via a mortar finite element space on a coarse grid scale, while the equations in the coarse elements (or subdomains) are discretized on a fine grid scale.
Todd Arbogast +3 more
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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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Multiscale finite element method–triple grid model for simulation of groundwater flows
Yantu gongcheng xuebao, 2022 The traditional finite element method often requires fine element grids to describle the heterogeneity of medium to ensure the accuracy for numerical modeling of groundwater, which leads to a large amount of calculation consumption. The multiscale finite
XIE Yi-fan 1, 2, XIE Zhen-ze 1, 2, WU Ji-chun 3, ZHANG Wei 4, XIE Chun-hong 5, LU Chun-hui 1, 2, 6
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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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