On a local Fourier analysis for overlapping block smoothers on triangular grids
Abstract
A general local Fourier analysis for overlapping block smoothers on triangular grids is presented. This analysis is explained in a general form for its application to problems with different discretizations. This tool is demonstrated for two different problems: a stabilized linear finite element discretization of Stokes equations and an edge-based discretization of the curl-curl operator by lowest-order N\'ed\'elec finite element method. In this latter, special Fourier modes have to be considered in order to perform the analysis. Numerical results comparing two- and three-grid convergence factors predicted by the local Fourier analysis to real asymptotic convergence factors are presented to confirm the predictions of the analysis and show their usefulness.
Cite
@article{arxiv.1510.04341,
title = {On a local Fourier analysis for overlapping block smoothers on triangular grids},
author = {Carmen Rodrigo and Francisco J. Gaspar and Francisco J. Lisbona},
journal= {arXiv preprint arXiv:1510.04341},
year = {2015}
}