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 intended to be comprehensive.
Chung, Eric +2 more
arxiv +12 more sources
Generalized multiscale finite element method for highly heterogeneous compressible flow [PDF]
arXiv, 2022 In this paper, we study the generalized multiscale finite element method (GMsFEM) for single phase compressible flow in highly heterogeneous porous media. We follow the major steps of the GMsFEM to construct permeability dependent offline basis for fast coarse-grid simulation.
Shubin Fu, Eric T. Chung, Lina Zhao
arxiv +7 more sources
Generalized Multiscale Finite Element Method for Elastic Wave Propagation in the Frequency Domain [PDF]
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
doaj +5 more sources
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
core +6 more sources
A Generalized Multiscale Finite Element Method for Poroelasticity Problems I: Linear Problems [PDF]
arXiv, 2015 In this paper, we consider the numerical solution of poroelasticity problems that are of Biot type and develop a general algorithm for solving coupled systems. We discuss the challenges associated with mechanics and flow problems in heterogeneous media.
Brown, Donald L., Vasilyeva, Maria
arxiv +8 more sources
An Online Generalized Multiscale Finite Element Method for Unsaturated Filtration Problem in Fractured Media [PDF]
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
doaj +3 more sources
Online Coupled Generalized Multiscale Finite Element Method for the Poroelasticity Problem in Fractured and Heterogeneous Media [PDF]
Fluids, 2021 In this paper, we consider the poroelasticity problem in fractured and heterogeneous media. The mathematical model contains a coupled system of equations for fluid pressures and displacements in heterogeneous media.
Aleksei Tyrylgin +4 more
doaj +3 more sources
Cluster-based Generalized Multiscale Finite Element Method for elliptic PDEs with random coefficients [PDF]
, 2017 We propose a generalized multiscale finite element method (GMsFEM) based on clustering algorithm to study the elliptic PDEs with random coefficients in the multi-query setting. Our method consists of offline and online stages. In the offline stage, we construct a small number of reduced basis functions within each coarse grid block, which can then be ...
Chung, Eric T. +3 more
arxiv +5 more sources
Generalized Multiscale Finite Element Method and Balanced Truncation for Parameter-Dependent Parabolic Problems [PDF]
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
doaj +3 more sources
Mixed Generalized Multiscale Finite Element Method for a Simplified Magnetohydrodynamics Problem in Perforated Domains [PDF]
Computation, 2020 In this paper, we consider a coupled system of equations that describes simplified magnetohydrodynamics (MHD) problem in perforated domains. We construct a fine grid that resolves the perforations on the grid level in order to use a traditional ...
Valentin Alekseev +4 more
doaj +3 more sources