منابع مشابه
Numerical homogenization methods
Numerical homogenization methods Synonyms multiscale methods for homogenization problems, upscaling methods, representative volume element methods Definition Numerical homogenization methods are techniques for finding numerical solutions of partial differential equations (PDEs) with rapidly oscillating coefficients (multiple scales). In mathematical analysis, homogenization can be defined as a ...
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A numerical homogenization procedure for elliptic differential equations is presented. It is based on wavelet decompositions of discrete operators in fine and coarse scale components followed by the elimination of the fine scale contributions. If the operator is in divergence form, this is preserved by the homogenization procedure. For periodic problems, results similar to classical effective c...
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(1) −∇ · (a(x)∇u(x)) = f(x) in Ω, u(x) = 0 on ∂Ω, where Ω is a bounded convex polyhedron in Rd, with d ≤ 3. Zero Dirichlet boundary conditions are taken here for simplicity and we emphasize that other boundary conditions can be treated with the multiscale method described below. We also note that while we discuss linear elliptic problems, the multiscale method (and the a-priori analysis) can be...
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In this paper we review various numerical homogenization methods for monotone parabolic problems with multiple scales. The spatial discretisation is based on finite element methods and the multiscale strategy relies on the heterogeneous multiscale method. The time discretization is performed by several classes of Runge-Kutta methods (strongly A−stable or explicit stabilized methods). We discuss...
متن کاملNumerical Methods for Homogenization of Maxwell’s Equations
When the wavelength is much larger than the typical scale of the microstructure in a material, it is possible to de£ne effective or homogenized material coef£cients. Two numerical methods for the determination of the homogenized, coef£cients are compared. Numerical examples, where extreme properties of the effective material are achieved in the two dimensional case, are presented.
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ژورنال
عنوان ژورنال: Discrete and Continuous Dynamical Systems - Series S
سال: 2016
ISSN: 1937-1632
DOI: 10.3934/dcdss.201605i