Selecting a practical successive over relaxation parameter for a Particle­-In­-Cell model

Abstract

The rate of convergence of the Successive Over­Relaxation (SOR) method depends on the choice of SOR Parameter, ω. It is shown that the SOR method as a Poisson Solver in the Particle­in­Cell (PIC), has a practical SOR parameter, ω_p, that is independent of the number of particles contained by the system. A method that speeds up the selection of this ω_p is proposed. For a 16x16 Plasma PIC system, using 7 test points and an increment of s = 0.03215, the ωp selected by the method is 1.71 which is equal to the ω_p determined from a parameter scan.