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Article Dans Une Revue ESAIM: Mathematical Modelling and Numerical Analysis Année : 2021

An iterative method for elliptic problems with rapidly oscillating coefficients

S. Armstrong
  • Fonction : Auteur
A. Hannukainen
  • Fonction : Auteur
T. Kuusi
  • Fonction : Auteur

Résumé

We introduce a new iterative method for computing solutions of elliptic equations with random rapidly oscillating coefficients. Similarly to a multigrid method, each step of the iteration involves different computations meant to address different length scales. However, we use here the homogenized equation on all scales larger than a fixed multiple of the scale of oscillation of the coefficients. While the performance of standard multigrid methods degrades rapidly under the regime of large scale separation that we consider here, we show an explicit estimate on the contraction factor of our method which is independent of the size of the domain. We also present numerical experiments which confirm the effectiveness of the method.

Dates et versions

hal-01728749 , version 1 (12-03-2018)

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S. Armstrong, A. Hannukainen, T. Kuusi, Jean-Christophe Mourrat. An iterative method for elliptic problems with rapidly oscillating coefficients. ESAIM: Mathematical Modelling and Numerical Analysis, 2021, ⟨10.1051/m2an/2020080⟩. ⟨hal-01728749⟩
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