Application of hierarchical matrix techniques to the homogenization of composite materials

Paul Cazeaux (1, 2) , Olivier Zahm (3)

1 LJLL - Laboratoire Jacques-Louis Lions
2 MCSS - Chair of Computational Mathematics and Simulation Science
3 GeM - Institut de Recherche en Génie Civil et Mécanique

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.

Domaines: Equations aux dérivées partielles [math.AP]

Paul Cazeaux, Olivier Zahm. Application of hierarchical matrix techniques to the homogenization of composite materials. 2013. ⟨hal-00922827⟩