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

James Brannick, Xiaozhe Hu, Carmen Rodrigo, Ludmil Zikatanov

Research output: Contribution to journalArticle

3 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)1-21
Number of pages21
JournalNumerical Mathematics
Volume8
Issue number1
DOIs
StatePublished - Jan 1 2015

All Science Journal Classification (ASJC) codes

  • Modeling and Simulation
  • Control and Optimization
  • Computational Mathematics
  • Applied Mathematics

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