Parallel multigrid technique: reduction to independent problems

There are two obvious reasons why a palallel multigrid algorithm may perform unsatisfactorily: load imbalance and communication overhead. Large communication overhead and processor idleness take place on very coarse grids. The paper represents the further development of the parallel robust multigrid technique based on the reduction of the finite-difference boundary value problem to a set of independent problems. Robust Multigrid Technique is a single grid algorithm used essential multigrid principle to minimize the number of the problem-dependent components. Usage of the same grid for the correction computing eliminates all problems with load imbalance and communication overhead on the coarse grids. In some cases volume of the stored data and execution time can be reduced and almost full parallelism can be obtained. Results of the numerical experiments with finite-difference scheme of the sixth approximation order are given.