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Collective symplectic integrators
Institute of Fundamental Sciences, Massey University, Palmerston North, New Zealand.
Department of Mathematical Sciences, Chalmers University of Technology, Gothenburg, Sweden.
Department of Mathematics, University of Bergen, Norway.ORCID-id: 0000-0003-3699-6244
2014 (engelsk)Inngår i: Nonlinearity, ISSN 0951-7715, E-ISSN 1361-6544, Vol. 27, nr 6, s. 1525-1542Artikkel i tidsskrift (Fagfellevurdert) Published
Abstract [en]

We construct symplectic integrators for Lie-Poisson systems. The integrators are standard symplectic (partitioned) Runge-Kutta methods. Their phase space is a symplectic vector space equipped with a Hamiltonian action with momentum map J whose range is the target Lie-Poisson manifold, and their Hamiltonian is collective, that is, it is the target Hamiltonian pulled back by J. The method yields, for example, a symplectic midpoint rule expressed in 4 variables for arbitrary Hamiltonians on so(3)*. The method specializes in the case that a sufficiently large symmetry group acts on the fibres of J, and generalizes to the case that the vector space carries a bifoliation. Examples involving many classical groups are presented.

sted, utgiver, år, opplag, sider
Institute of Physics Publishing (IOPP), 2014. Vol. 27, nr 6, s. 1525-1542
Emneord [en]
symplectic integrators, Lie-Poisson systems, reduction
HSV kategori
Identifikatorer
URN: urn:nbn:se:umu:diva-89403DOI: 10.1088/0951-7715/27/6/1525ISI: 000337159700020OAI: oai:DiVA.org:umu-89403DiVA, id: diva2:720446
Tilgjengelig fra: 2014-05-29 Laget: 2014-05-29 Sist oppdatert: 2018-06-07bibliografisk kontrollert

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