| Abstract: |
| Computing the homogenized properties of random materials is often very expensive. A standard approach consists in considering a large domain, and solving the so-called corrector problem on that domain, submitted to e.g. periodic boundary conditions. Because the computational domain is finite, the approximate homogenized properties are random, and fluctuate from one realization of the microstructure to another. We have recently introduced several efficient numerical approaches to reduce the statistical noise. These approaches allow to compute the expectation of the homogenized coefficients in a more efficient manner than brute force Monte Carlo methods.
Beside the (averaged) behavior of the material response on large space scales (which is given by its homogenized limit), another question of interest is to understand how much this response fluctuates around its coarse approximation, before the homogenized regime is attained. More generally, we aim at understanding which parameters of the distribution of the material coefficients affect the distribution of the response, and whether it is possible to compute that latter distribution without resorting to a brute force Monte Carlo approach.
This talk, based on joint works with P.-L. Rothe, will review the recent progresses made on these questions, both from the theoretical and numerical viewpoints. |
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