Volume 11, Issue 4
Elements of Mathematical Foundations for Numerical Approaches for Weakly Random Homogenization Problems

A. Anantharaman & C. Le Bris

Commun. Comput. Phys., 11 (2012), pp. 1103-1143.

Published online: 2012-04

Preview Full PDF 104 793
Export citation
  • Abstract

This work is a follow-up to our previous work [2]. It extends and complements, both theoretically and experimentally, the results presented there. Under consideration is the homogenization of a model of a weakly random heterogeneous material. The material consists of a reference periodic material randomly perturbed by another periodic material, so that its homogenized behavior is close to that of the reference material. We consider laws for the random perturbations more general than in [2]. We prove the validity of an asymptotic expansion in a certain class of settings. We also extend the formal approach introduced in [2]. Our perturbative approach shares common features with a defect-type theory of solid state physics. The computational efficiency of the approach is demonstrated.


  • Keywords

  • AMS Subject Headings

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{CiCP-11-1103, author = {A. Anantharaman and C. Le Bris}, title = {Elements of Mathematical Foundations for Numerical Approaches for Weakly Random Homogenization Problems}, journal = {Communications in Computational Physics}, year = {2012}, volume = {11}, number = {4}, pages = {1103--1143}, abstract = {

This work is a follow-up to our previous work [2]. It extends and complements, both theoretically and experimentally, the results presented there. Under consideration is the homogenization of a model of a weakly random heterogeneous material. The material consists of a reference periodic material randomly perturbed by another periodic material, so that its homogenized behavior is close to that of the reference material. We consider laws for the random perturbations more general than in [2]. We prove the validity of an asymptotic expansion in a certain class of settings. We also extend the formal approach introduced in [2]. Our perturbative approach shares common features with a defect-type theory of solid state physics. The computational efficiency of the approach is demonstrated.


}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.030610.010411s}, url = {http://global-sci.org/intro/article_detail/cicp/7403.html} }
TY - JOUR T1 - Elements of Mathematical Foundations for Numerical Approaches for Weakly Random Homogenization Problems AU - A. Anantharaman & C. Le Bris JO - Communications in Computational Physics VL - 4 SP - 1103 EP - 1143 PY - 2012 DA - 2012/04 SN - 11 DO - http://dor.org/10.4208/cicp.030610.010411s UR - https://global-sci.org/intro/cicp/7403.html KW - AB -

This work is a follow-up to our previous work [2]. It extends and complements, both theoretically and experimentally, the results presented there. Under consideration is the homogenization of a model of a weakly random heterogeneous material. The material consists of a reference periodic material randomly perturbed by another periodic material, so that its homogenized behavior is close to that of the reference material. We consider laws for the random perturbations more general than in [2]. We prove the validity of an asymptotic expansion in a certain class of settings. We also extend the formal approach introduced in [2]. Our perturbative approach shares common features with a defect-type theory of solid state physics. The computational efficiency of the approach is demonstrated.


A. Anantharaman & C. Le Bris. (1970). Elements of Mathematical Foundations for Numerical Approaches for Weakly Random Homogenization Problems. Communications in Computational Physics. 11 (4). 1103-1143. doi:10.4208/cicp.030610.010411s
Copy to clipboard
The citation has been copied to your clipboard