Results 21 to 30 of about 27,980 (243)
Generalized multiscale finite element method for the steady state linear Boltzmann equation [PDF]
Multiscale Modeling & Simulation, 2019 The Boltzmann equation, as a model equation in statistical mechanics, is used to describe the statistical behavior of a large number of particles driven by the same physics laws. Depending on the media and the particles to be modeled, the equation has slightly different forms.
Eric T. Chung +3 more
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A Generalized Multiscale Finite Element Method for poroelasticity problems II: nonlinear coupling [PDF]
Journal of Computational and Applied Mathematics, 2015 In this paper, we consider the numerical solution of some nonlinear poroelasticity problems that are of Biot type and develop a general algorithm for solving nonlinear coupled systems.
Abdulle +18 more
core +7 more sources
Mixed Generalized Multiscale Finite Element Method for Darcy-Forchheimer Model [PDF]
Mathematics, 2019 In this paper, the solution of the Darcy-Forchheimer model in high contrast heterogeneous media is studied. This problem is solved by a mixed finite element method (MFEM) on a fine grid (the reference solution), where the pressure is approximated by piecewise constant elements; meanwhile, the velocity is discretized by the lowest order Raviart-Thomas ...
Denis Spiridonov +4 more
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Multiscale Empirical Interpolation for Solving Nonlinear PDEs using\n Generalized Multiscale Finite Element Methods [PDF]
, 2014 In this paper, we propose a multiscale empirical interpolation method for solving nonlinear multiscale partial differential equations. The proposed method combines empirical interpolation techniques and local multiscale methods, such as the Generalized Multiscale Finite Element Method (GMsFEM).
Victor M. Calo +3 more
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Online conservative generalized multiscale finite element method for flow models [PDF]
, 2020 In this paper, we consider an online enrichment procedure using the Generalized Multiscale Finite Element Method (GMsFEM) in the context of a two-phase flow model in heterogeneous porous media. The coefficient of the elliptic equation is referred to as the permeability and is the main source of heterogeneity within the model.
Yiran Wang +3 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
doaj +1 more source
Online Multiscale Finite Element Simulation of Thermo-Mechanical Model with Phase Change
Computation, 2023 This paper presents a thermo-mechanical model with phase transition considering changes in the mechanical properties of the medium. The proposed thermo-mechanical model is described by a system of partial differential equations for temperature and ...
Dmitry Ammosov, Maria Vasilyeva
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Multiscale Multiphysics Modeling of the Infiltration Process in the Permafrost
Mathematics, 2021 In this work, we design a multiscale simulation method based on the Generalized Multiscale Finite Element Method (GMsFEM) for numerical modeling of fluid seepage under permafrost condition in heterogeneous soils.
Sergei Stepanov +2 more
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Mixed Generalized Multiscale Finite Element Methods and Applications [PDF]
Multiscale Modeling & Simulation, 2015 In this paper, we present a mixed Generalized Multiscale Finite Element Method (GMsFEM) for solving flow in heterogeneous media. Our approach constructs multiscale basis functions following a GMsFEM framework and couples these basis functions using a mixed finite element method, which allows us to obtain a mass conservative velocity field. To construct
Chung, Eric T. +2 more
openaire +4 more sources
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 +1 more source