Computing homogenized coefficients via multiscale representation and hierarchical hybrid grids

Antti Hannukainen, Jean Christophe Mourrat, Harmen T. Stoppels

Research output: Contribution to journalArticlepeer-review

Abstract

We present an efficient method for the computation of homogenized coefficients of divergence-form operators with random coefficients. The approach is based on a multiscale representation of the homogenized coefficients. We then implement the method numerically using a finite-element method with hierarchical hybrid grids, which is a semi-implicit method allowing for significant gains in memory usage and execution time. Finally, we demonstrate the efficiency of our approach on two- and three-dimensional examples, for piecewise-constant coefficients with corner discontinuities. For moderate ellipticity contrast and for a precision of a few percentage points, our method allows to compute the homogenized coefficients on a laptop computer in a few seconds, in two dimensions, or in a few minutes, in three dimensions.

Original languageEnglish (US)
Pages (from-to)S149-S185
JournalESAIM: Mathematical Modelling and Numerical Analysis
Volume55
DOIs
StatePublished - 2021

Keywords

  • Hierarchical hybrid grids
  • Homogenization
  • Multiscale method

ASJC Scopus subject areas

  • Analysis
  • Numerical Analysis
  • Modeling and Simulation
  • Computational Mathematics
  • Applied Mathematics

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