Mesh Independent Superlinear PCG Rates Via Compact-Equivalent Operators

Authors:
Owe Axelsson;János Karátson
Affiliations:
-;-
Venue:
SIAM Journal on Numerical Analysis
Year:
2007

Citing 0
Cited 8

A mesh independent superlinear algorithm for some nonlinear nonsymmetric elliptic systems

Computers & Mathematics with Applications
On Superlinear PCG Methods for FDM Discretizations of Convection-Diffusion Equations

Numerical Analysis and Its Applications
Mesh independent superlinear convergence of an inner-outer iterative method for semilinear elliptic interface problems

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Mesh Independent Convergence Rates Via Differential Operator Pairs

Large-Scale Scientific Computing
Equivalent operator preconditioning for elliptic problems with nonhomogeneous mixed boundary conditions

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An Analysis of Equivalent Operator Preconditioning for Equation-Free Newton-Krylov Methods

SIAM Journal on Numerical Analysis
Original article: Macro-elementwise preconditioning methods

Mathematics and Computers in Simulation
Reaching the superlinear convergence phase of the CG method

Journal of Computational and Applied Mathematics

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Abstract

The subject of the paper is the mesh independent convergence of the preconditioned conjugate gradient (PCG) method for nonsymmetric elliptic problems. The approach of equivalent operators is involved, in which one uses the discretization of another suitable elliptic operator as preconditioning matrix. By introducing the notion of compact-equivalent operators, it is proved that for a wide class of elliptic problems the superlinear convergence of the obtained PCG method is mesh independent under finite element discretizations; that is, the rate of superlinear convergence is given in the form of a sequence which is mesh independent and is determined only by the elliptic operators.