The analysis of multigrid algorithms for nonsymmetric and indefinite elliptic problems

James H. Bramble, Joseph E. Pasciak, Jinchao Xu

Research output: Contribution to journalArticle

53 Citations (Scopus)

Abstract

We prove some new estimates for the convergence of multigrid algorithms applied to nonsymmetric and indefinite elliptic boundary value problems. We provide results for the so-called 'symmetric' multigrid schemes. We show that for the variable v-cycle and the m;-cycle schemes, multigrid algorithms with any amount of smoothing on the finest grid converge at a rate that is independent of the number of levels or unknowns, provided that the initial grid is sufficiently fine. We show that the v-cycle algorithm also converges (under appropriate assumptions on the oarsest grid) but at a rate which may deteriorate as the number of levels increases. This deterioration for the m-cycle may occur even in the case of full elliptic regularity. Finally, the results of numerical experiments are given which illustrate the convergence behavior suggested by the theory.

Original languageEnglish (US)
Pages (from-to)389-414
Number of pages26
JournalMathematics of Computation
Volume51
Issue number184
DOIs
StatePublished - Jan 1 1988

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Elliptic Problems
Cycle
Grid
Elliptic Regularity
Converge
Boundary value problems
Deterioration
Elliptic Boundary Value Problems
Smoothing
Numerical Experiment
Unknown
Experiments
Estimate

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory
  • Computational Mathematics
  • Applied Mathematics

Cite this

Bramble, James H. ; Pasciak, Joseph E. ; Xu, Jinchao. / The analysis of multigrid algorithms for nonsymmetric and indefinite elliptic problems. In: Mathematics of Computation. 1988 ; Vol. 51, No. 184. pp. 389-414.
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The analysis of multigrid algorithms for nonsymmetric and indefinite elliptic problems. / Bramble, James H.; Pasciak, Joseph E.; Xu, Jinchao.

In: Mathematics of Computation, Vol. 51, No. 184, 01.01.1988, p. 389-414.

Research output: Contribution to journalArticle

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