A multigrid conjugate gradient method

In this paper, we describe a new approach to combine the conjugate gradient method and the multigrid method. This approach simultaneously constructs conjugate new correction directions based on restricted gradients. The computational amount is O(N), where N is the number of unknowns. The algorithm is easy to implement. It only requires restriction and prolongation operators, matrix vector multiplications on several levels, and scalar products. Therefore, the algorithm can be applied to accelerate a multilevel algorithm with slow convergence.Numerical results for Poisson's equation with jumping coefficients and a Stokes type equation are presented.