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.
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Applied Numerical Mathematics
Scientific Computing

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