Superlinear convergence estimates for a conjugate gradient method for the biharmonic equation

Raymond H. CHAN*, Thomas K. DELILLO, Mark A. HORN

*Corresponding author for this work

Research output: Journal PublicationsJournal Article (refereed)peer-review

5 Citations (Scopus)

Abstract

The method of Muskhelishvili for solving the biharmonic equation using conformal mapping is investigated. In [R. H. Chan, T. K. DeLillo, and M. A. Horn, SIAM J. Sci. Comput., 18 (1997), pp. 1571-1582] it was shown, using the Hankel structure, that the linear system in [N. I. Muskhelishvili, Some Basic Problems of the Mathematical Theory of Elasticity, Noordhoff, Groningen, the Netherlands] is the discretization of the identity plus a compact operator, and therefore the conjugate gradient method will converge superlinearly. Estimates are given here of the superlinear convergence in the cases when the boundary curve is analytic or in a Hölder class.

Original languageEnglish
Pages (from-to)139-147
Number of pages9
JournalSIAM Journal on Scientific Computing
Volume19
Issue number1
DOIs
Publication statusPublished - Jan 1998
Externally publishedYes

Keywords

  • Biharmonic equation
  • Conjugate gradient method
  • Hankel matrices
  • Numerical conformal mapping

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