A Numerical Approach Related to Defect-Type Theories for Some Weakly Random Problems in Homogenization
We present in this paper an approach for computing the homogenized behavior of a medium that is a small random perturbation of a periodic reference material. The random perturbation we consider is, in a sense made precise in our work, a rare event at the microscopic level. It, however, affects the m...
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| Veröffentlicht in: | Multiscale modeling & simulation 2011-01, Vol.9 (2), p.513-544 |
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| creator | Anantharaman, A. Le Bris, C. |
| description | We present in this paper an approach for computing the homogenized behavior of a medium that is a small random perturbation of a periodic reference material. The random perturbation we consider is, in a sense made precise in our work, a rare event at the microscopic level. It, however, affects the macroscopic properties of the material, and we indeed provide a method to compute the first- and second-order corrections. To this end, we formally establish an asymptotic expansion of the macroscopic properties. Our perturbative approach shares common features with a defect-type theory of solid state physics. The computational efficiency of the approach is demonstrated. [PUBLICATION ABSTRACT] |
| doi_str_mv | 10.1137/10079639X |
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| ispartof | Multiscale modeling & simulation, 2011-01, Vol.9 (2), p.513-544 |
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| source | SIAM Journals Online |
| subjects | Analysis of PDEs Composite materials Homogenization Mathematics Partial differential equations Random variables |
| title | A Numerical Approach Related to Defect-Type Theories for Some Weakly Random Problems in Homogenization |
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