On Superlinear PCG Methods for FDM Discretizations of Convection-Diffusion Equations

Authors:
János Karátson;Tamás Kurics
Affiliations:
Department of Applied Analysis and Computational Mathematics, ELTE University, Budapest, Hungary H-1117;Department of Applied Analysis and Computational Mathematics, ELTE University, Budapest, Hungary H-1117
Venue:
Numerical Analysis and Its Applications
Year:
2009

Citing 9
Cited 0

A generalized conjugate gradient, least square method

Numerische Mathematik
Preconditioning and boundary conditions

SIAM Journal on Numerical Analysis
On the theory of equivalent operators and application to the numerical solution of uniformly elliptic partial differential equations

Advances in Applied Mathematics
A taxonomy for conjugate gradient methods

SIAM Journal on Numerical Analysis
Optimal equivalent preconditioners

SIAM Journal on Numerical Analysis
Iterative solution methods

Iterative solution methods
Superlinearly convergent CG methods via equivalent preconditioning for nonsymmetric elliptic operators

Numerische Mathematik
Superlinearly convergent PCG algorithms for some nonsymmetric elliptic systems

Journal of Computational and Applied Mathematics
Mesh Independent Superlinear PCG Rates Via Compact-Equivalent Operators

SIAM Journal on Numerical Analysis

Quantified Score

Hi-index	0.00

Visualization

Abstract

The numerical solution of linear convection-diffusion equations is considered. Finite difference discretization leads to an algebraic system solved by a suitable preconditioned CG method, where the preconditioning approach is based on equivalent operators. Our goal is to study the superlinear convergence of the preconditioned CG iteration and to find mesh independent behaviour on a model problem. This is an analogue of previous results where FEM discretization was used.