A computational method of solving free-boundary problems in vortex dynamics

Optimal harvesting strategy based on rearrangements of functions

“…Fortunately, for the current problem we can devise an algorithm based on the approach of Eydeland and Turkington [ET88], which was also applied to a rearrangement problem by Elcrat and Nicolio [EN95]. The pseudocode in Fig.…”

The Onset of Instability in Exact Vortex Rings with Swirl

“…Furtions which reduce to two independent variables. These special solutions are assumed to be independent of time ther, the method of proof was extended to a numerical method for generating these rings in [12]; see also [11,38]. except for translation.…”

“…To reduce the exThe existence theorem of Turkington [37] was based on a variational formulation of the problem. A closely related pense of the summation in the Biot-Savart Law, we use a fast summation method of the type developed by numerical method for finding solutions was developed by Eydeland and Turkington [11,12,38]. A constrained varia-Greengard and Rokhlin [15,16]; the version we use here is due to Buttke [7].…”

Finite element approximation of a non-Lipschitz nonlinear eigenvalue problem

“…One can view (1.3) as a free boundary problem since f2 + = {x s Q : u(x)> g} and F = d/2 + are unknown. It would be of interest to analyse the finite element approximation of (1.3) when ƒ is given by (1.2) with p s [0, 1) ; this being a model vortex problem, see Eydeland and Turkington (1988) for example. In this paper we analyse the finite element approximation of a simpler problem, the nonlinear eigenvalue problem (P (A )) : Find (A, u(A )) e U x HQ(S2), u ^ 0, such that (1.1a) holds, where ƒ is given by (1.2) withp G (0, 1).…”