Results 31 to 40 of about 5,178 (170)
High-Order Multiscale Finite Element Method for Elliptic Problems [PDF]
Multiscale Modeling & Simulation, 2014 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hesthaven, Jan S. +2 more
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A convergence analysis of Generalized Multiscale Finite Element Methods [PDF]
Journal of Computational Physics, 2019 In this paper, we consider an approximation method, and a novel general analysis, for second-order elliptic differential equations with heterogeneous multiscale coefficients. We obtain convergence of the Generalized Multi-scale Finite Element Method (GMsFEM) method that uses local eigenvectors in its construction.
Eduardo Abreu, Ciro Díaz, Juan Galvis
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Abstract and Applied Analysis, 2014 A new finite difference scheme, the development of the finite difference heterogeneous multiscale method (FDHMM), is constructed for simulating saturated water flow in random porous media.
Fulai Chen, Li Ren
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Analysis of porosity influence on the effective moduli of ceramic matrix PZT composite using the simplified finite element model [PDF]
Journal of Advanced Dielectrics, 2019 The problem of determining the effective moduli of a ceramic matrix piezocomposite with respect to multiscale porosity was considered. To solve the homogenization problem, the method of effective moduli in the standard formulation, the finite element ...
Anna Kudimova, Andrey Nasedkin
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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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MathematicsIn this study, the extended finite element method (XFEM) was integrated into the generalized multiscale finite element method with global–local enrichment (GFEMgl) to simulate 2D heat conduction in highly heterogeneous materials (i.e., matrixes with ...
Guangzhong Liu +3 more
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Prediction of Discretization of GMsFEM Using Deep Learning
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 +5 more
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Learning Algorithms for Coarsening Uncertainty Space and Applications to Multiscale Simulations
Mathematics, 2020 In this paper, we investigate and design multiscale simulations for stochastic multiscale PDEs. As for the space, we consider a coarse grid and a known multiscale method, the generalized multiscale finite element method (GMsFEM).
Zecheng Zhang +3 more
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Reduced Basis Multiscale Finite Element Methods for Elliptic Problems [PDF]
Multiscale Modeling & Simulation, 2015 Summary: In this paper, we propose reduced basis multiscale finite element methods (RB-MsFEMs) for elliptic problems with highly oscillating coefficients. The method is based on MsFEMs with local test functions that encode the oscillatory behavior (see [\textit{G. Allaire} and \textit{R. Brizzi}, Multiscale Model. Simul. 4, No.
Hesthaven, Jan S. +2 more
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Journal of Applied Mathematics, 2013 We discuss several stabilized finite element methods, which are penalty, regular, multiscale enrichment, and local Gauss integration method, for the steady incompressible flow problem with damping based on the lowest equal-order finite element space pair.
Jilian Wu, Pengzhan Huang, Xinlong Feng
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