Multiple coarse grid acceleration for multiscale multigrid computation

The multiscale multigrid method uses an iterative refinement procedure with the Richardson extrapolation technique to obtain a higher order solution. The computational cost for the iterative refinement procedure may be significant for some ill conditioned coefficient matrices. In this paper, we proposed an alternative strategy using multiple coarse grids to eliminate the iterative refinement procedure, and thus accelerate the multiscale multigrid computation. Numerical investigations show that our multiple coarse grid computing strategy is more efficient and scalable than the iterative refinement procedure. The multiscale multigrid method with multiple coarse grid strategy is used to solve two dimensional (2D) Poisson equation and convection diffusion equation, but the idea can be used to solve other partial differential equations.