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

Journal Article · Thu Jan 01 00:00:00 EST 1998 · SIAM Journal on Scientific Computing

DOI:https://doi.org/10.1137/S1064827596303570· OSTI ID:599810

Chan, R H ^[1]; Delillo, T K; Horn, M A ^[2]

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1. Chinese Univ. of Hong Kong, Shatin (Hong Kong). Dept. of Mathematics
2. Wichita State Univ., KS (United States). Dept. of Mathematics and Statistics

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 Hoelder class.

• Sponsoring Organization: USDOE, Washington, DC (United States); National Science Foundation, Washington, DC (United States)
• DOE Contract Number: FG02-92ER25124
• OSTI ID: 599810
• Journal Information: SIAM Journal on Scientific Computing, Vol. 19, Issue 1; Other Information: PBD: Jan 1998
• Country of Publication: United States
• Language: English

Related Subjects

99 MATHEMATICS
COMPUTERS
INFORMATION SCIENCE
MANAGEMENT
LAW
MISCELLANEOUS
CONFORMAL MAPPING
BOUNDARY-VALUE PROBLEMS
CALCULATION METHODS
CONVERGENCE
MATRICES