An offline-online strategy for multiscale problems with random defects
Artikel i vetenskaplig tidskrift, 2022

In this paper, we propose an offline-online strategy based on the Localized Orthogonal Decomposition (LOD) method for elliptic multiscale problems with randomly perturbed diffusion coefficient. We consider a periodic deterministic coefficient with local defects that occur with probability p. The offline phase pre-computes entries to global LOD stiffness matrices on a single reference element (exploiting the periodicity) for a selection of defect configurations. Given a sample of the perturbed diffusion the corresponding LOD stiffness matrix is then computed by taking linear combinations of the pre-computed entries, in the online phase. Our computable error estimates show that this yields a good approximation of the solution for small p, which is illustrated by extensive numerical experiments. This makes the proposed technique attractive already for moderate sample sizes in a Monte Carlo simulation.

Multiscale method

Random perturbations

Numerical homogenization

Finite elements


Axel Målqvist

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik

Barbara Verfürth

Karlsruher Institut für Technologie (KIT)

Mathematical Modelling and Numerical Analysis

0764-583X (ISSN) 1290-3841 (eISSN)

Vol. 56 1 237-260



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