576 citations · 638 across the 16 of their papers we have counts for
17 papers
Gauge equivalence and transdimensional perturbation: point vortices
George W. Patrick
There is an explicit resolution of the Poisson reduction of four planar point vortices, in the case that three of the vortex strengths are equal and the total vorticity is zero. Th…
On theoretical upper limits for valid timesteps of implicit ODE methods
K. R. Green, G. W. Patrick, R. J. Spiteri
Implicit methods for the numerical solution of initial-value problems may admit multiple solutions at any given time step. Accordingly, their nonlinear solvers may converge to any…
The geometry of convergence in numerical analysis
George W. Patrick
The domains of mesh functions are strict subsets of the underlying space of continuous independent variables. Spaces of partial maps between topological spaces admit topologies whi…
The vector field of a rolling rigid body
George W. Patrick
Nonholonomic systems are variational models commonly used for mechanical systems with ideal no-slip constraints. This note provides a differential-geometric derivation of the nonho…
Error analysis of variational integrators of unconstrained Lagrangian systems
George W. Patrick, Charles Cuell
A complete error analysis of variational integrators is obtained, by blowing up the discrete variational principles, all of which have a singularity at zero time-step. Divisions by…
Geometric discrete analogues of tangent bundles and constrained Lagrangian systems
Charles Cuell, George W. Patrick
Discretizing variational principles, as opposed to discretizing differential equations, leads to discrete-time analogues of mechanics, and, systematically, to geometric numerical i…