Special quasirandom structures: A selection approach for stochastic homogenization

Claude Le Bris 1 , Frédéric Legoll 2 , and William Minvielle 2
  • 1 École des Ponts and INRIA, 6 et 8 avenue Blaise Pascal, 77455 Marne-La-Vallée Cedex 2, France
  • 2 École des Ponts and INRIA, 6 et 8 avenue Blaise Pascal, 77455 Marne-La-Vallée Cedex 2, France

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 , , , 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.

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