English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this paper, we propose an offline-online strategy based on the LocalizedOrthogonal Decomposition (LOD) method for elliptic multiscale problems withrandomly perturbed diffusion coefficient. We consider a periodic deterministiccoefficient with local defects that occur with probability $p$. The offlinephase pre-computes entries to global LOD stiffness matrices on a singlereference element (exploiting the periodicity) for a selection of defectconfigurations. Given a sample of the perturbed diffusion the corresponding LODstiffness matrix is then computed by taking linear combinations of thepre-computed entries, in the online phase. Our computable error estimates showthat this yields a good coarse-scale approximation of the solution for small$p$, which is illustrated by extensive numerical experiments. This makes theproposed technique attractive already for moderate sample sizes in a MonteCarlo simulation.

An offline-online strategy for multiscale problems with random defects