A minimal-variable symplectic integrator on spheres

DOI10.1090/mcom/3153zbMath1364.37166arXiv1402.3334OpenAlexW1509133757MaRDI QIDQ2981779

Klas Modin, Olivier Verdier, Robert I. Mclachlan

Publication date: 10 May 2017

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1402.3334

zbMATH Keywords

Hamiltonian systemsintegratordiscretisationgeodesic midpoint method

Mathematics Subject Classification ID

Related Items (12)

Integrability of point-vortex dynamics via symplectic reduction: a survey ⋮ Geometry of discrete-time spin systems ⋮ A minimal-variable symplectic method for isospectral flows ⋮ Geometric integration on symmetric spaces ⋮ B-stability of numerical integrators on Riemannian manifolds ⋮ Lie-Poisson methods for isospectral flows ⋮ Vortex pairs on the triaxial ellipsoid: axis equilibria stability ⋮ Collective heavy top dynamics ⋮ Energy-preserving methods on Riemannian manifolds ⋮ A Casimir preserving scheme for long-time simulation of spherical ideal hydrodynamics ⋮ Hamiltonians and canonical coordinates for spinning particles in curved space-time ⋮ On the linear stability of a vortex pair equilibrium on a Riemann surface of genus zero

Cites Work

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• Geometric generalisations of SHAKE and RATTLE
• Point vortices on the sphere: stability of symmetric relative equilibria
• Symplectic integrators for classical spin systems
• B-series methods are exactly the affine equivariant methods
• Dynamics of vorticity at a sphere
• Integrators for Lie-Poisson dynamical systems
• Discrete versions of some classical integrable systems and factorization of matrix polynomials
• Almost Poisson integration of rigid body systems
• KAM theorem of symplectic algorithms for Hamiltonian systems
• Geometric integration on spheres and some interesting applications
• Discrete integrable systems. Proceedings of the international CIMPA school, Pondicherry, India, February 2--14, 2003
• Motion of three point vortices on a sphere
• The motion of three point vortices on a sphere
• Stability of Runge-Kutta Methods for Trajectory Problems
• The fascinating world of the Landau–Lifshitz–Gilbert equation: an overview
• Point vortex dynamics: A classical mathematics playground
• Symplectic geometry
• Loop groups, discrete versions of some classical integrable systems, and rank 2 extensions
• Invariants of real low dimension Lie algebras
• Generalized Hamiltonian Dynamics
• Discrete Euler-Poincaré and Lie-Poisson equations
• Symplectic Partitioned Runge–Kutta Methods for Constrained Hamiltonian Systems
• Collective symplectic integrators
• Collective Lie-Poisson integrators on R3
• Geometric integrators for ODEs
• Geometric Numerical Integration

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