Please use this identifier to cite or link to this item:
|Operator-splitting methods via the Zassenhaus product formula
Iterative solver method
Parabolic differential equations
|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.
|Appears in Collections:
|WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection
Show full item record
Items in GCRIS Repository are protected by copyright, with all rights reserved, unless otherwise indicated.