Special quasirandom structures: A selection approach for stochastic homogenization
Abstract
We adapt and study a variance reduction approach for the homogenization of elliptic equations in divergence form. The approach, borrowed from atomistic simulations and solid-state science [23], [24], [25], consists in selecting random realizations that best satisfy some statistical properties (such as the volume fraction of each phase in a composite material) usually only obtained asymptotically. We study the approach theoretically in some simplified settings (one-dimensional setting, perturbative setting in higher dimensions), and numerically demonstrate its efficiency in more general cases.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Feb 17, 2016
- Source ID
- 10.1515/mcma-2016-0101
Entities
People
- Claude Le Bris
- Frederic Legoll
- William Minvielle
Organizations
- Agence Nationale de la Recherche
- Office of Naval Research
- École des Ponts ParisTech