Selecting a practical successive over relaxation parameter for a particle-in-cell method


The rate of convergence of the Successive Over-Relaxation (SOR) method depends on the choice of SOR Parameter, ω. It is shown that the SOR method as a Poisson Solver in the Particle-in-Cell (PIC), has a practical SOR parameter, ωp, that is independent of the number of particles contained by the system. A method that speeds up the selection of this ωp 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 ωp determined from a parameter scan.