The paper represents the main directions of development of the parallel classic multigrid algorithms and discusses their disadvantages. The possibility of efficient parallelization of smoothing iterations at the levels of coarse grids is shown using the Robust Multigrid Technique. Then multigrid structure is used for developing hybrid multigrid method. The paper describes estimations of speed-up and efficiency of different parallel multigrid algorithms as well as the results of numerical experiments.
Martynenko S. Parallel multigrid algorithms. Маthematical Modeling and Coтputational Methods, 2015, №2 (6), pp. 105-120