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A low-rank power iteration scheme for neutron transport critically problems

Kusch, Jonas; Whewell, Benjamin; McClarren, Ryan; Frank, Martin ORCID iD icon

Abstract:

Computing effective eigenvalues for neutron transport often requires a fine numerical resolution. The main challenge of such computations is the high memory effort of classical solvers, which limits the accuracy of chosen discretizations. In this work, we derive a method for the computation of effective eigenvalues when the underlying solution has a low-rank structure. This is accomplished by utilizing dynamical low-rank approximation (DLRA), which is an efficient strategy to derive time evolution equations for low-rank solution representations. The main idea is to interpret the iterates of the classical inverse power iteration as pseudo-time steps and apply the DLRA concepts in this framework. In our numerical experiment, we demonstrate that our method significantly reduces memory requirements while achieving the desired accuracy. Analytic investigations show that the proposed iteration scheme inherits the convergence speed of the inverse power iteration, at least for a simplified setting.


Volltext §
DOI: 10.5445/IR/1000141707
Veröffentlicht am 10.01.2022
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Angewandte und Numerische Mathematik (IANM)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht/Preprint
Publikationsmonat/-jahr 01.2022
Sprache Englisch
Identifikator ISSN: 2365-662X
KITopen-ID: 1000141707
Verlag Karlsruher Institut für Technologie (KIT)
Umfang 19 S.
Serie CRC 1173 Preprint ; 2022/4
Projektinformation SFB 1173/2 (DFG, DFG KOORD, SFB 1173/2 2019)
Externe Relationen Siehe auch
Schlagwörter dynamical low-rank approximation, kinetic equations, neutron transport, unconventional integrator
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