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An offline-online strategy for multiscale problems with random defects

Målqvist, Axel; Verfürth, Barbara

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 $p$. 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 $p$. Moreover, extensive numerical experiments illustrate that relative errors of a few percent are achieved up to at least $p = 0.1$. This makes the proposed technique attractive already for moderate sample sizes in a Monte Carlo simulation.

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Volltext §
DOI: 10.5445/IR/1000129328
Veröffentlicht am 05.02.2021
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Angewandte und Numerische Mathematik (IANM)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht/Preprint
Publikationsmonat/-jahr 02.2021
Sprache Englisch
Identifikator ISSN: 2365-662X
KITopen-ID: 1000129328
Verlag Karlsruher Institut für Technologie (KIT)
Umfang 22 S.
Serie CRC 1173 Preprint ; 2021/7
Projektinformation SFB 1173/2 (DFG, DFG KOORD, SFB 1173/2 2019)
Externe Relationen Siehe auch
Schlagwörter numerical homogenization, multiscale method, finite elements, random perturbations
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