Multiscale Materials Science: A Mathematical Approach to the Role of Defects and Uncertainty
Final rept. 1 Apr 2012-31 Mar 2015
PARIS INST OF TECHNOLOGY MARNE LA VALLEE (FRANCE) NATIONAL SCHOOL OF BRIDGES AND ROADS
Pagination or Media Count:
We focus on developing affordable numerical methods in the context of stochastic homogenization. Our aim is to compute the homogenized coefficients that represent the behavior of the material at a macroscopic scale. Such computations are usually very expensive. To decrease their cost, we consider a variance reduction technique, namely the control variate technique, and numerically demonstrate its efficiency. We also address questions related to non-periodic modelling of multiscale materials. A typical example is that of a periodic material with a superimposed defect in one periodic cell.
- Theoretical Mathematics