This thesis presents a novel Eulerian numerical method to compute global isochrons of a stable periodic orbit in high dimensions. The approach is to formulate the asymptotic phase as a solution to a first order boundary value problem and solve the resulting Hamilton-Jacobi equation with the parallel Fast Sweeping Method. All isochrons are then given as isocontours of the phase. To demonstrate the method, it is applied to the Hodgkin-Huxley equations and a model of a dopaminergic neuron which exhibits mixed mode oscillations. Results show that this Eulerian scheme is an efficient, accurate method for computing the asymptotic phase of a periodic dynamical system. Furthermore, by computing phase on a Cartesian grid, it is simple to compute the gradient of phase, and thus, compute an ''almost phaseless'' target set for the purposes of desynchronization of a system of oscillators.