Some remarks on a coupling method for the practical computation of homogenized coefficients

TL;DR

This paper improves a computational coupling method for efficiently calculating homogenized coefficients of media with highly oscillatory properties, combining mathematical formalization, algorithm enhancements, and numerical validation.

Contribution

The paper provides a formal mathematical framework and algorithmic improvements for a coupling method to compute homogenized coefficients more efficiently.

Findings

Enhanced algorithmic efficiency demonstrated through numerical results

Mathematical formalization clarifies the coupling approach

Numerical results show improved accuracy over original method

Abstract

We numerically investigate, and improve upon, a computational approach originally introduced in [Cottereau, IJNME 2013] which aims at evaluating the effective coefficient of a medium modelled by a highly oscillatory coefficient. This computational approach is based on a Arlequin type coupling. It combines the original fine-scale description of the medium (modelled by an oscillatory coefficient) with an effective description (modelled by a constant coefficient) and optimizes upon the coefficient of the effective medium to best fit the response of the actual heterogeneous medium using a purely homogeneous medium. We present here a mathematical formalization of the approach along with various improvements of the algorithms, in order to obtain a procedure as efficient as possible. Representative numerical results demonstrate the added value of our approach in comparison to the original approach.