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

Tags

Fields of Study

  • Mathematics

Readers

  • Computational Fluid Dynamics (CFD)
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Statistical inference.