Please use this identifier to cite or link to this item: https://hdl.handle.net/11147/10751
Title: Operator-splitting methods via the Zassenhaus product formula
Authors: Geiser, Juergen
Tanoğlu, Gamze
Tanoğlu, Gamze
Izmir Institute of Technology. Mathematics
Keywords: Operator-splitting method
Iterative solver method
Weighting methods
Zassenhaus product
Parabolic differential equations
Issue Date: 2011
Publisher: Elsevier Ltd.
Abstract: In this paper, we contribute an operator-splitting method improved by the Zassenhaus product. Zassenhaus products are of fundamental importance for the theory of Lie groups and Lie algebras. While their applications in physics and physical chemistry are important, novel applications in CFD (computational fluid dynamics) arose based on the fact that their sparse matrices can be seen as generators of an underlying Lie algebra. We apply this to classical splitting and the novel Zassenhaus product formula. The underlying analysis for obtaining higher order operator-splitting methods based on the Zassenhaus product is presented. The benefits of dealing with sparse matrices, given by spatial discretization of the underlying partial differential equations, are due to the fact that the higher order commutators are very quickly computable (their matrix structures thin out and become nilpotent). When applying these methods to convection-diffusion-reaction equations, the benefits of balancing time and spatial scales can be used to accelerate these methods and take into account these sparse matrix structures. The verification of the improved splitting methods is done with numerical examples. Finally, we conclude with higher order operator-splitting methods. (C) 2010 Elsevier Inc. All rights reserved.
URI: https://doi.org/10.1016/j.amc.2010.11.007
https://hdl.handle.net/11147/10751
ISSN: 0096-3003
Appears in Collections:WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection

Show full item record

CORE Recommender

SCOPUSTM   
Citations

12
checked on Sep 25, 2021

WEB OF SCIENCETM
Citations

8
checked on Sep 25, 2021

Page view(s)

44
checked on Sep 27, 2021

Google ScholarTM

Check

Altmetric


Items in GCRIS Repository are protected by copyright, with all rights reserved, unless otherwise indicated.