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Volume 8, Issue 1
Local Fourier Analysis for Edge-Based Discretizations on Triangular Grids

Carmen Rodrigo, Francisco Sanz, Francisco J. Gaspar & Francisco J. Lisbona

DOI: 10.4208/nmtma.2015.w07si

Numer. Math. Theor. Meth. Appl., 8 (2015), pp. 78-96.

Published online: 2015-08

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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.

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@Article{NMTMA-8-78, author = {Carmen Rodrigo, Francisco Sanz, Francisco J. Gaspar and Francisco J. Lisbona}, title = {Local Fourier Analysis for Edge-Based Discretizations on Triangular Grids}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2015}, volume = {8}, number = {1}, pages = {78--96}, 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.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2015.w07si}, url = {http://global-sci.org/intro/article_detail/nmtma/12400.html} }
TY - JOUR T1 - Local Fourier Analysis for Edge-Based Discretizations on Triangular Grids AU - Carmen Rodrigo, Francisco Sanz, Francisco J. Gaspar & Francisco J. Lisbona JO - Numerical Mathematics: Theory, Methods and Applications VL - 1 SP - 78 EP - 96 PY - 2015 DA - 2015/08 SN - 8 DO - http://doi.org/10.4208/nmtma.2015.w07si UR - https://global-sci.org/intro/article_detail/nmtma/12400.html KW - AB -

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.

Carmen Rodrigo, Francisco Sanz, Francisco J. Gaspar and Francisco J. Lisbona. (2015). Local Fourier Analysis for Edge-Based Discretizations on Triangular Grids. Numerical Mathematics: Theory, Methods and Applications. 8 (1). 78-96. doi:10.4208/nmtma.2015.w07si
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