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Sparse compression of expected solution operators

Feischl, Michael; Peterseim, Daniel


We show that the expected solution operator of prototypical linear elliptic partial differential operators with random coefficients is well approximated by a computable sparse matrix. This result is based on a random localized orthogonal multiresolution decomposition of the solution space that allows both the sparse approximate inversion of the random operator represented in this basis as well as its stochastic averaging. The approximate expected solution operator can be interpreted in terms of classical Haar wavelets. When combined with a suitable sampling approach for the expectation, this construction leads to an efficient method for computing a sparse representation of the expected solution operator.

Volltext §
DOI: 10.5445/IR/1000086887
Veröffentlicht am 23.10.2018
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Angewandte und Numerische Mathematik (IANM)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht/Preprint
Publikationsjahr 2018
Sprache Englisch
Identifikator ISSN: 2365-662X
KITopen-ID: 1000086887
Verlag Karlsruher Institut für Technologie (KIT)
Umfang 18 S.
Serie CRC 1173 ; 2018/21
Schlagwörter uncertainty quantification, Monte Carlo, stochastic homogenisation,localized orthogonal decomposition
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