Papers › An offline-online strategy for multiscale problems with random defects
An offline-online strategy for multiscale problems with random defects
Axel Målqvist, Barbara Verfürth
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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 coarse-scale 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.
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