Two-sided bounds on the convergence rate of two-level methods

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Abstract

In this paper, we prove two-sided bounds on the convergence rate of a standard two-level subspace correction method. We then apply these estimates to show that a two-level method with point-wise smoother for variational problem in H0 (curl) does not have optimal convergence rate. This result justifies the conclusion, observed numerically and reported in the literature, that a point relaxation as a smoother does not lead to an optimal multigrid method. In fact, we show that for such problems using a well-conditioned smoother will always lead to a method that is not optimal.

Original languageEnglish (US)
Pages (from-to)439-454
Number of pages16
JournalNumerical Linear Algebra with Applications
Volume15
Issue number5 SPEC. ISS.
DOIs
StatePublished - Jun 1 2008

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory
  • Applied Mathematics

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