Journal ArticleDOI
Computation of effective resistivity in materials with microinclusions by a heterogeneous multiscale finite element method
TLDR
In this article, a numerical method to obtain an effective electrical resistivity of heterogeneous media under the influence of a direct current was proposed, where the heterogeneous multiscale finite element method was used to solve the direct problem of simulation of an electrostatic field.About:
This article is published in Physical Mesomechanics.The article was published on 2017-10-01. It has received 7 citations till now. The article focuses on the topics: Finite element method.read more
Citations
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Journal ArticleDOI
A vectorized assembly-free FEM solver for image-based numerical homogenization
Journal ArticleDOI
A GPU implementation of the PCG method for large-scale image-based finite element analysis in heterogeneous periodic media
TL;DR: In this article , a massively parallel Preconditioned Conjugate Gradient (PCG) solver is used for finite element analyses of heat conduction and linear elasticity on image-based models.
Journal ArticleDOI
Determination of thermal, stiffness and electrical effective tensors in composite media
TL;DR: In this paper , the problem of calculating effective anisotropic thermal, electric and mechanical properties of composite media is considered and numerical algorithms for the homogenization of heterogeneous media based on the upscaling technique and effective medium theory are proposed.
Proceedings ArticleDOI
Numerical Determination of the Effective Elasticity Tensor of an Heterogeneous Solid
TL;DR: In this paper, a numerical method based on the heterogeneous multiscale finite element method with polyhedral supports was proposed to determine the effective elasticity tensor of three-dimensional objects with the complex internal structure.
Book ChapterDOI
Application of the Heterogeneous Multiscale Finite Element Method for Modelling the Compressibility of Porous Media
TL;DR: In this paper , the authors used the heterogeneous multiscale finite element method on polyhedron supports for the numerical simulation of porous media, as a rule, are non-periodic and essentially multiscales.
References
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Journal ArticleDOI
A Multiscale Finite Element Method for Elliptic Problems in Composite Materials and Porous Media
Thomas Y. Hou,Xiao-Hui Wu +1 more
TL;DR: This paper studies a multiscale finite element method for solving a class of elliptic problems arising from composite materials and flows in porous media, which contain many spatial scales and proposes an oversampling technique to remove the resonance effect.
Book
Electromagnetic mixing formulas and applications
TL;DR: In this article, the mathematical analysis of macroscopic dielectric and magnetic properties of geophysical, biological and other materials, including special reference to chiral and nonlinear material, the effects of structure and anistrophy are discussed in detail.
Journal ArticleDOI
The Heterognous Multiscale Methods
Weinan E,Björn Engquist +1 more
TL;DR: The heterogenous multiscale method (HMM) as mentioned in this paper is a general methodology for the efficient numerical computation of problems with multiscales and multiphysics on multigrids.
Journal ArticleDOI
Generalized multiscale finite element methods (GMsFEM)
TL;DR: The main idea of the proposed approach is to construct a small dimensional local solution space that can be used to generate an efficient and accurate approximation to the multiscale solution with a potentially high dimensional input parameter space.
Journal ArticleDOI
Convergence of a multiscale finite element method for elliptic problems with rapidly oscillating coefficients
TL;DR: This paper provides a detailed convergence analysis of the multiscale finite element method for solving second order elliptic equations with rapidly oscillating coefficients under the assumption that the oscillating coefficient is of two scales and is periodic in the fast scale.