In this work, incomplete factorization techniques are used as smoothers within a geometric multigrid algorithm on triangular grids. A local Fourier analysis is proposed to study the smoothing properties of these methods, as well as the asymptotic convergence of the whole multigrid procedure. With this purpose, two-and three-grid local Fourier analysis are performed. Several two-dimensional diffusion problems, including different kinds of anisotropy are considered to demonstrate the robustness of this type of methods.
Multigrid, Incomplete factorization, ILU smoother, Local Fourier analysis
Null option (theme 11)
Applied Numerical Mathematics
Scientific Computing

Pinto, M.A.V, Rodrigo, C, Gaspar, F.J, & Oosterlee, C.W. (2016). On the robustness of ILU smoothers on triangular grids. Applied Numerical Mathematics, 106, 37–52. doi:10.1016/j.apnum.2016.02.007