Two-scale extensions for non-periodic coefficients

TL;DR

This paper introduces a two-scale extension method for modeling non-homogeneous media with rapidly oscillating coefficients, enhancing homogenization techniques for better analysis of complex materials.

Contribution

It proposes new ways to construct two-scale extensions and explores their properties and connections to homogenization theory.

Findings

Multiple methods for constructing two-scale extensions are presented.

The properties of these extensions are analyzed in relation to homogenization.

The approach improves understanding of non-periodic media with oscillatory properties.

Abstract

We consider non-homogeneous media with properties which can be characterized by rapidly oscillated coefficients. For such coefficients we define a notion of two-scale extension, present several ways to construct two-scale extensions, discuss their properties and relation to homogenization