Local Fourier analysis of multigrid methods with polynomial smoothers and aggressive coarsening

Abstract. We focus on the study of multigrid methods with aggressive coarsening and polynomial smoothers for the solution of the linear systems corresponding to finite dif-ference/element discretizations of the Laplace equation. Using local Fourier analysis we determine automatically the optimal values for the parameters involved in defining the polynomial smoothers and achieve fast convergence of cycles with aggressive coarsen-ing. We also present numerical tests supporting the theoretical results and the heuristic ideas. The methods we introduce are highly parallelizable and efficient multigrid algo-rithms on structured and semi-structured grids in two and three spatial dimensions