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Local Fourier Analysis for Edge-Based Discretizations on Triangular Grids

Published online by Cambridge University Press:  03 March 2015

Carmen Rodrigo ,
Francisco Sanz ,
Francisco J. Gaspar  and
Francisco J. Lisbona
Carmen Rodrigo*
Affiliation:
Department of Applied Mathematics, University of Zaragoza, C/ Maria de Luna 3, 50018, Zaragoza, Spain
Francisco Sanz
Affiliation:
BIFI University of Zaragoza, C/ Pedro Cerbuna 12, 50009, Zaragoza, Spain
Francisco J. Gaspar
Affiliation:
Department of Applied Mathematics, University of Zaragoza, C/ Pedro Cerbuna 12, 50009, Zaragoza, Spain
Francisco J. Lisbona
Affiliation:
Department of Applied Mathematics, University of Zaragoza, C/ Pedro Cerbuna 12, 50009, Zaragoza, Spain
*
*Email addresses: carmenr@unizar.es (C. Rodrigo), frasanz@bifi.es (F. Sanz), fjgaspar@unizar.es (F. J. Gaspar), lisbona@unizar.es (F. J. Lisbona)
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Abstract

In this paper, we present a local Fourier analysis framework for analyzing the different components within multigrid solvers for edge-based discretizations on triangular grids. The different stencils associated with edges of different orientation in a triangular mesh make this analysis special. The resulting tool is demonstrated for the vector Laplace problem discretized by mimetic finite difference schemes. Results from the local Fourier analysis, as well as experimentally obtained results, are presented to validate the proposed analysis.

Keywords

65F1065N2265N55Multigridlocal Fourier analysisedge-based discretizationsmimetic finite differences

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Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 8 , Issue 1 , February 2015 , pp. 78 - 96
Copyright
Copyright © Global-Science Press 2015 

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