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On dynamical low-rank integrators for matrix differential equations

Schrammer, Stefan ORCID iD icon 1
1 Institut für Angewandte und Numerische Mathematik (IANM), Karlsruher Institut für Technologie (KIT)

Abstract (englisch):

This thesis is concerned with dynamical low-rank integrators for matrix differential equations, typically stemming from space discretizations of partial differential equations. We first construct and analyze a dynamical low-rank integrator for second-order matrix differential equations, which is based on a Strang splitting and the projector-splitting integrator, a dynamical low-rank integrator for first-order matrix
differential equations proposed by Lubich and Osedelets in 2014. For the analysis, we derive coupled recursive inequalities, where we express the global error of the scheme in terms of a time-discretization error and a low-rank error contribution. The first can be treated with Taylor series expansion of the exact solution. For the latter, we make use of an induction argument and the convergence result derived by Kieri, Lubich, and Walach in 2016 for the projector-splitting integrator.
From the original method, several variants are derived which are tailored to, e.g., stiff or highly oscillatory second-order problems. After discussing details on the implementation of dynamical low-rank schemes, we turn towards rank-adaptivity. ... mehr


Volltext §
DOI: 10.5445/IR/1000148853
Veröffentlicht am 15.08.2022
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Angewandte und Numerische Mathematik (IANM)
Publikationstyp Hochschulschrift
Publikationsdatum 15.08.2022
Sprache Englisch
Identifikator KITopen-ID: 1000148853
Verlag Karlsruher Institut für Technologie (KIT)
Umfang vii, 111 S.
Art der Arbeit Dissertation
Fakultät Fakultät für Mathematik (MATH)
Institut Institut für Angewandte und Numerische Mathematik (IANM)
Prüfungsdatum 13.07.2022
Projektinformation SFB 1173/2 (DFG, DFG KOORD, SFB 1173/2 2019)
Schlagwörter dynamical low-rank approximation, dynamical low-rank integrators, matrix differential equations, numerical analysis, error analysis, time integration, second-order matrix differential equation
Relationen in KITopen
Referent/Betreuer Hochbruck, Marlis
Neher, Markus
Einkemmer, Lukas
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