In this paper, we study numerical homogenization methods based on integral equations. Our work is motivated by materials such as concrete, modeled as composites structured as randomly distributed inclusions imbedded in a matrix. We investigate two integral reformulations of the corrector problem to be solved, namely the equivalent inclusion method based on the Lippmann-Schwinger equation, and a method based on boundary integral equations. The fully populated matrices obtained by the discretization of the integral operators are successfully dealt with using the H-matrix format.
@article{arxiv.1401.0185,
title = {Application of Hierarchical Matrix Techniques To The Homogenization of Composite Materials},
author = {Paul Cazeaux and Olivier Zahm},
journal= {arXiv preprint arXiv:1401.0185},
year = {2014}
}