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Local Fourier Analysis of Multigrid Methods with Polynomial Smoothers and Aggressive Coarsening

Published online by Cambridge University Press:  03 March 2015

James Brannick ,
Xiaozhe Hu ,
Carmen Rodrigo  and
Ludmil Zikatanov
James Brannick
Affiliation:
Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, USA
Xiaozhe Hu*
Affiliation:
Department of Mathematics, Tufts University, 503 Boston Ave., Medford, MA 02155, USA
Carmen Rodrigo
Affiliation:
Department of Applied Mathematics, University of Zaragoza, C/ Maria de Luna 3, 50018, Zaragoza, Spain
Ludmil Zikatanov
Affiliation:
Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, USA Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 8, 1113 Sofia, Bulgaria
*
*Email addresses: brannick@psu.edu (J. Brannick), Xiaozhe.Hu@tufts.edu (X. Hu), carmenr@unizar.es (C. Rodrigo), ludmil@psu.edu (L. Zikatanov)
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Abstract

We focus on the study of multigrid methods with aggressive coarsening and polynomial smoothers for the solution of the linear systems corresponding to finite difference/element discretizations of the Laplace equation. Using local Fourier analysis we determine automatically the optimal values for the parameters involved in defining the polynomial smoothers and achieve fast convergence of cycles with aggressive coarsening. We also present numerical tests supporting the theoretical results and the heuristic ideas. The methods we introduce are highly parallelizable and efficient multigrid algorithms on structured and semi-structured grids in two and three spatial dimensions.

Keywords

65F1065N2265N55Multigridlocal Fourier analysispolynomial smoothersaggressive coarsening
Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 8 , Issue 1 , February 2015 , pp. 1 - 21
Copyright
Copyright © Global-Science Press 2015 

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