Comparative convergence analysis of nonlinear AMLI-cycle multigrid

Xiaozhe Hu, Panayot S. Vassilevski, Jinchao Xu

Research output: Contribution to journalArticle

11 Scopus citations

Abstract

The main purpose of this paper is to provide a comprehensive convergence analysis of the nonlinear algebraic multilevel iteration (AMLI)-cycle multigrid (MG) method for symmetric positive definite problems. Based on classical assumptions for approximation and smoothing properties, we show that the nonlinear AMLI-cycle MG method is uniformly convergent. Furthermore, under only the assumption that the smoother is convergent, we show that the nonlinear AMLI-cycle method is always better (or not worse) than the respective V-cycle MG method. Finally, numerical experiments are presented to illustrate the theoretical results.

Original languageEnglish (US)
Pages (from-to)1349-1369
Number of pages21
JournalSIAM Journal on Numerical Analysis
Volume51
Issue number2
DOIs
StatePublished - 2013

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

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