Local Fourier analysis for cell-centered multigrid methods on triangular grids

This work is focused on the design of efficient multigrid methods for discretizations on Voronoi meshes associated with regular refinements of acute triangles. For this purpose, a special local Fourier analysis for this type of discretizations is developed. This analysis helps us to obtain appropriate novel smoothers depending on the geometry of the grid. A two- and three-grid analysis are performed to analyze the behavior of the multigrid methods. Numerical test calculations validate the theoretical predictions. Furthermore, the application of this analysis for the solution of more real problems, by using semi-structured grids, is shown.