A parallel 2-level 4-color SOR method

A 2-level 4-color SOR method is proposed for the solution of the 9-point discretization of the Poisson equation on a square in parallel. Instead of examining the Jacobi iteration matrix in the space domain, we consider an equivalent but much simpler 4-color iteration matrix in the frequency domain. A 2-level SOR method is introduced to increase the convergence rate for the frequency-domain iteration matrix. At a first level, the red and orange points, and then the black and green points are treated as groups, and a block SOR iteration is performed on these two groups. At a second level, another SOR iteration is used to decouple values of the solution at the red and orange points, and then at the black and green points. The optimal relaxation parameters for these two relaxation levels are determined.