An offline-online strategy for multiscale problems with random defects
Abstract
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 . 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 coarse-scale approximation of the solution for small , which is illustrated by extensive numerical experiments. This makes the proposed technique attractive already for moderate sample sizes in a Monte Carlo simulation.
Cite
@article{arxiv.2102.01635,
title = {An offline-online strategy for multiscale problems with random defects},
author = {Axel Målqvist and Barbara Verfürth},
journal= {arXiv preprint arXiv:2102.01635},
year = {2021}
}