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Collective symplectic integrators

Robert McLachlan ; Klas Modin (Institutionen för matematiska vetenskaper, matematik) ; Olivier Verdier
Nonlinearity (0951-7715). Vol. 27 (2014), 6, p. 1525-1542.
[Artikel, refereegranskad vetenskaplig]

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 $\mathfrak{so}(3)^*$ . 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.

Denna post skapades 2014-06-09. Senast ändrad 2014-09-29.
CPL Pubid: 198992


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Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, matematik (2005-2016)


Numerisk analys

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