Special quasirandom structures: A selection approach for stochastic homogenization

Le Bris Claude (), Legoll Frédéric () and Minvielle William ()
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Le Bris Claude: École des Ponts and INRIA, 6 et 8 avenue Blaise Pascal, 77455 Marne-La-Vallée Cedex 2, France
Legoll Frédéric: École des Ponts and INRIA, 6 et 8 avenue Blaise Pascal, 77455 Marne-La-Vallée Cedex 2, France
Minvielle William: École des Ponts and INRIA, 6 et 8 avenue Blaise Pascal, 77455 Marne-La-Vallée Cedex 2, France

Monte Carlo Methods and Applications, 2016, vol. 22, issue 1, 25-54

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.

Keywords: Stochastic homogenization; elliptic partial differential equations; variance reduction; selection approach (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1515/mcma-2016-0101

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