KIT | KIT-Bibliothek | Impressum | Datenschutz

Dynamical low-rank approximation for Burgers’ equation with uncertainty

Kusch, Jonas; Ceruti, Gianluca; Einkemmer, Lukas; Frank, Martin

Abstract:

Quantifying uncertainties in hyperbolic equations is a source of several challenges. First, the solution forms shocks leading to oscillatory behaviour in the numerical approximation of the solution. Second, the number of unknowns required for an effective discretization of the solution grows exponentially with the dimension of the uncertainties, yielding high computational costs and large memory requirements. An efficient representation of the solution via adequate basis functions permits to tackle these difficulties. The generalized polynomial chaos (gPC) polynomials allow such an efficient representation when the distribution of the uncertainties is known. These distributions are usually only available for input uncertainties such as initial conditions, therefore the efficiency of this ansatz can get lost during runtime. In this paper, we make use of the dynamical low-rank approximation (DLRA) to obtain a memory-wise efficient solution approximation on a lower dimensional manifold. We investigate the use of the matrix projector-splitting integrator and the unconventional integrator for dynamical low-rank approximation, deriving separate time evolution equations for the spatial and uncertain basis functions, respectively. ... mehr


Volltext §
DOI: 10.5445/IR/1000132636
Veröffentlicht am 12.05.2021
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Angewandte und Numerische Mathematik (IANM)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht/Preprint
Publikationsmonat/-jahr 05.2021
Sprache Englisch
Identifikator ISSN: 2365-662X
KITopen-ID: 1000132636
Verlag Karlsruher Institut für Technologie (KIT)
Umfang 24 S.
Serie CRC 1173 Preprint ; 2021/20
Projektinformation SFB 1173/2 (DFG, DFG KOORD, SFB 1173/2 2019)
Externe Relationen Siehe auch
Schlagwörter uncertainty quantification, conservation laws, hyperbolic, intrusive UQ methods, dynamical low-rank approximation, matrix projector-splitting integrator, unconventional integrator
Nachgewiesen in arXiv
Relationen in KITopen
KIT – Die Forschungsuniversität in der Helmholtz-Gemeinschaft
KITopen Landing Page