303 citations · 717 across the 42 of their papers we have counts for
5 papers · 1 filter
Geometric properties of Kahan's method
Elena Celledoni, Robert I McLachlan, Brynjulf Owren +1
We show that Kahan's discretization of quadratic vector fields is equivalent to a Runge--Kutta method. When the vector field is Hamiltonian on either a symplectic vector space or a…
High order semi-Lagrangian methods for the incompressible Navier-Stokes equations
Elena Celledoni, Bawfeh Kingsley Kometa, Olivier Verdier
We propose a class of semi-Lagrangian methods of high approximation order in space and time, based on spectral element space discretizations and exponential integrators of Runge-Ku…
An introduction to Lie group integrators -- basics, new developments and applications
Elena Celledoni, Håkon Marthinsen, Brynjulf Owren
We give a short and elementary introduction to Lie group methods. A selection of applications of Lie group integrators are discussed. Finally, a family of symplectic integrators on…
The minimal stage, energy preserving Runge-Kutta method for polynomial Hamiltonian systems is the Averaged Vector Field method
Elena Celledoni, Brynjulf Owren, Yajuan Sun
No Runge-Kutta method can be energy preserving for all Hamiltonian systems. But for problems in which the Hamiltonian is a polynomial, the Averaged Vector Field (AVF) method can be…
Preserving energy resp. dissipation in numerical PDEs using the "Average Vector Field" method
E. Celledoni, V. Grimm, R. I. McLachlan +4
We give a systematic method for discretizing Hamiltonian partial differential equations (PDEs) with constant symplectic structure, while preserving their energy exactly. The same m…