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arXiv · 1510.04341

On a local Fourier analysis for overlapping block smoothers on triangular grids

Carmen Rodrigo·Francisco J. Gaspar·Francisco J. Lisbona
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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.

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Carmen Rodrigo, Francisco J. Gaspar, Francisco J. Lisbona. 2015-10-14. On a local Fourier analysis for overlapping block smoothers on triangular grids. https://arxiv.org/abs/1510.04341

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