A multigrid conjugate gradient method Original Research Article

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)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 Poissonʹs equation with jumping coefficients and a Stokes type equation are presented.