An efficient red–black skewed extrapolation cascadic multigrid method for two-dimensional Poisson equation

We present a red–black skewed extrapolation cascadic multigrid (SkECMG) method to solve the Poisson equation in two dimensions based on the modified standard and skewed five-point finite difference discretization. With the help of the extrapolation technique, we develop a new extrapolation operator. Applying this proposed extrapolation operator for the second-order finite difference solutions on the current and previous coarse grid, we can design a fourth-order initial value for the iterative solver on the next finer grid. The red–black Gauss–Seidel method is adopted as a smoother which is conducive to parallel implementation. Moreover, we discuss a new sifting method as a stopping criterion to reduce the number of smoothing iterations. The numerical experiment is conducted on the square domain to verify that our SkECMG algorithm can achieve high efficiency and keep less cost simultaneously.