The recently introduced needle problem approach for the homogenization of non-periodic problems was originally designed for the homogenization of elliptic problems. After a short review of the needle problem approach we demonstrate in this note how the stationary results can be transferred to time-dependent problems. The standard parabolic problem of the corresponding heat equation in a heterog...

Numerical homogenization tries to approximate solutions of elliptic partial differential equations with strongly oscillating coefficients by the solution of localized problems over small subregions. We develop and analyze a rapidly convergent iterative method for numerical homogenization that shares this feature with existing approaches and is modeled after the Schwarz method. The method is hig...

Based on the small parameter asymptotic homogenization theory, this article adopts the technology of digitized cell-based finite element method (DCB-FEM) to establish the digital cell-based mechanics analysis model of three-dimensional 4-directional braided composite material, analyzes and calculates the equivalent elasticity performance of 3D braided composite material using homogenization met...

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...

We present a Hilbert space perspective to homogenization of standard linear evolutionary boundary value problems in mathematical physics and provide a unified treatment for (non-)periodic homogenization problems in thermodynamics, elasticity, electro-magnetism and coupled systems thereof. The approach permits the consideration of memory problems as well as differential-algebraic equations. We s...

Homogenization theory is concerned with the task of extracting effective material parameters for composite media in the limit where the applied wavelength is large compared to the microstructure. Usually, this is analyzed in the extreme limit where the wavelength is infinite, but in this paper we present the framework of a method which deals with wavelengths that are comparable to the microstru...

We present a novel approach for a combined homogenization and registration technique. Medical image data is often disturbed by inhomogeneities from staining, illumination or attenuation. State-of-theart approaches tackle homogenization and registration separately. Our new method attacks both troublemakers simultaneously. It is modeled as a minimization problem of a functional consisting of a di...

Seal surface topography typically consists of global-scale geometric features as well as local-scale roughness details and homogenization-based approaches are, therefore, readily applied. These provide for resolving the global scale (large domain) with a relatively coarse mesh, while resolving the local scale (small domain) in high detail. As the total flow decreases, however, the flow pattern ...

A multiple-scattering theory is applied to study the homogenization of clusters of elastic cylinders distributed in a isotropic lattice and embedded in a viscous fluid. Asymptotic relations are derived and employed to obtain analytical formulas for the effective parameters of homogenized clusters in which the underlying lattice has a low filling fraction. It is concluded that such clusters beha...