Embedded Zassenhaus Expansion to Splitting Schemes : Theory and Multiphysics Applications
Author
Source
International Journal of Differential Equations
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-11, 11 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-09-24
Country of Publication
Egypt
No. of Pages
11
Main Subjects
Abstract EN
We present some operator splitting methods improved by the use of the Zassenhaus product and designed for applications to multiphysics problems.
We treat iterative splitting methods that can be improved by means of the Zassenhaus product formula, which is a sequential splitting scheme.
The main idea for reducing the computation time needed by the iterative scheme is to embed fast and cheap Zassenhaus product schemes, since the computation of the commutators involved is very cheap, since we are dealing with nilpotent matrices.
We discuss the coupling ideas of iterative and sequential splitting techniques and their convergence.
While the iterative splitting schemes converge slowly in their first iterative steps, we improve the initial convergence rates by embedding the Zassenhaus product formula.
The applications are to multiphysics problems in fluid dynamics.
We consider phase models in computational fluid dynamics and analyse how to obtain higher order operator splitting methods based on the Zassenhaus product.
The computational benefits derive from the use of sparse matrices, which arise from the spatial discretisation of the underlying partial differential equations.
Since the Zassenhaus formula requires nearly constant CPU time due to its sparse commutators, we have accelerated the iterative splitting schemes.
American Psychological Association (APA)
Geiser, Juergen. 2013. Embedded Zassenhaus Expansion to Splitting Schemes : Theory and Multiphysics Applications. International Journal of Differential Equations،Vol. 2013, no. 2013, pp.1-11.
https://search.emarefa.net/detail/BIM-462718
Modern Language Association (MLA)
Geiser, Juergen. Embedded Zassenhaus Expansion to Splitting Schemes : Theory and Multiphysics Applications. International Journal of Differential Equations No. 2013 (2013), pp.1-11.
https://search.emarefa.net/detail/BIM-462718
American Medical Association (AMA)
Geiser, Juergen. Embedded Zassenhaus Expansion to Splitting Schemes : Theory and Multiphysics Applications. International Journal of Differential Equations. 2013. Vol. 2013, no. 2013, pp.1-11.
https://search.emarefa.net/detail/BIM-462718
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-462718