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Explicit volume-preserving splitting methods for polynomial divergence-free vector fields

Content Provider	Springer Nature Link
Author	Zanna, Antonella Xue, Huiyan
Copyright Year	2012
Abstract	We present new, explicit, volume-preserving splitting methods for polynomial divergence-free vector fields of arbitrary degree (both positive and negative). The main idea is to decompose the divergence polynomial by means of an appropriate basis for polynomials: the monomial basis. For each monomial basis function, the split fields are then identified by collecting the appropriate terms in the vector field so that each split vector field is volume preserving. We show that each split field can be integrated exactly by analytical methods. Thus, the composition yields a volume preserving numerical method. Our numerical tests indicate that the methods compare favorably to standard integrators both in the quality of the numerical solution and the computational effort.
Ending Page	281
Page Count	17
Starting Page	265
File Format	PDF
ISSN	00063835
e-ISSN	15729125
Journal	BIT Numerical Mathematics
Issue Number	1
Volume Number	53
Language	English
Publisher	Springer Netherlands
Publisher Date	2012-07-18
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Splitting methods Computational Mathematics and Numerical Analysis Numeric Computing Symplectic integrators Mathematics Geometric integration Volume preservation Dynamical systems in numerical analysis
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Computer Networks and Communications Computational Mathematics Software

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