SUPERLINEAR CONVERGENCE ESTIMATES FOR A CONJUGATE GRADIENT METHOD FOR THE BIHARMONIC EQUATION

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Author(s)

Detail(s)

Original languageEnglish
Pages (from-to)139-147
Journal / PublicationSIAM Journal of Scientific Computing
Volume19
Issue number1
Publication statusPublished - Jan 1998
Externally publishedYes

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.

Research Area(s)

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