128 citations · 592 across the 51 of their papers we have counts for
4 papers · 2 filters
Symplectic integration of PDEs using Clebsch variables
Robert I McLachlan, Christian Offen, Benjamin K Tapley
Many PDEs (Burgers' equation, KdV, Camassa-Holm, Euler's fluid equations,...) can be formulated as infinite-dimensional Lie-Poisson systems. These are Hamiltonian systems on manifo…
Symplectic integration of boundary value problems
Robert I McLachlan, Christian Offen
Symplectic integrators can be excellent for Hamiltonian initial value problems. Reasons for this include their preservation of invariant sets like tori, good energy behaviour, none…
Preservation of bifurcations of Hamiltonian boundary value problems under discretisation
Robert I McLachlan, Christian Offen
We show that symplectic integrators preserve bifurcations of Hamiltonian boundary value problems and that nonsymplectic integrators do not. We provide a universal description of th…
Parallelisation, initialisation, and boundary treatments for the diamond scheme
Stephen R Marsland, Robert I McLachlan, Matthew C Wilkins
We study a class of general purpose linear multisymplectic integrators for Hamiltonian wave equations based on a diamond-shaped mesh. On each diamond, the PDE is discretized by a s…