39 citations · 312 across the 32 of their papers we have counts for
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A classification of volume preserving generating forms in R^3
Olivier Verdier, Huiyan Xue, Antonella Zanna
In earlier work, Lomeli and Meiss used a generalization of the symplectic approach to study volume preserving generating differential forms. In particular, for the c…
Multi-symplectic discretisation of wave map equations
David Cohen, Olivier Verdier
We present a new multi-symplectic formulation of constrained Hamiltonian partial differential equations, and we study the associated local conservation laws. A multi-symplectic dis…
B-series methods are exactly the affine equivariant methods
Robert I. McLachlan, Klas Modin, Hans Munthe-Kaas +1
Butcher series, also called B-series, are a type of expansion, fundamental in the analysis of numerical integration. Numerical methods that can be expanded in B-series are defined…
Integrators on homogeneous spaces: Isotropy choice and connections
Hans Munthe-Kaas, Olivier Verdier
We consider numerical integrators of ODEs on homogeneous spaces (spheres, affine spaces, hyperbolic spaces). Homogeneous spaces are equipped with a built-in symmetry. A numerical i…
Symplectic integrators for spin systems
Robert I. McLachlan, Klas Modin, Olivier Verdier
We present a symplectic integrator, based on the canonical midpoint rule, for classical spin systems in which each spin is a unit vector in . Unlike splitting methods…
A minimal-variable symplectic integrator on spheres
Robert I. McLachlan, Klas Modin, Olivier Verdier
We construct a symplectic, globally defined, minimal-coordinate, equivariant integrator on products of 2-spheres. Examples of corresponding Hamiltonian systems, called spin systems…