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...

Mechanical properties of rocks with inclusions, which may correspond to porous rocks under limiting conditions, are influenced by their shape, distributions, and intrinsic properties. Many different averaging methods such as homogenization, micro-mechanics and microstructure methods are proposed to estimate average thermo-hydro-mechanical properties of rocks. In this paper, the authors evaluate...

We consider homogenization problems in the framework of deterministic optimal control when the dynamics and running costs are completely different in two (or more) complementary domains of the space R . For such optimal control problems, the three first authors have shown that several value functions can be defined, depending, in particular, of the choice is to use only “regular strategies” or ...

| Approaches to the adequate homogenization of optical metamaterials are becoming more and more complex, primarily due to an increased understanding of the role of asymmetric electrical andmagnetic responses, in addition to thenonlocal effects of the surrounding medium, even in the simplest case of plane-wave illumination. The current trend in developing such advanced homogenization description...

In this paper we study the numerical homogenization of nonlinear random parabolic equations. This procedure is developed within a finite element framework. A careful choice of multiscale finite element bases and the global formulation of the problem on the coarse grid allow us to prove the convergence of the numerical method to the homogenized solution of the equation. The relation of the propo...