On the superlinear convergence of PCG algorithms: Numerical experiments for convection-diffusion equations

Authors:
Tamás Kurics
Affiliations:
Department of Applied Analysis and Computational Mathematics, ELTE University, H-1117 Budapest, Hungary
Venue:
Computers & Mathematics with Applications
Year:
2008

Citing 6
Cited 1

A generalized conjugate gradient, least square method

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Preconditioning second-order elliptic operators: experiment and theory

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Optimal equivalent preconditioners

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Abstract

The CGM is studied for nonsymmetric elliptic problems with both Dirichlet and mixed boundary conditions. The mesh independence of the convergence is an important property when symmetric part preconditioning is applied to the FEM discretizations of the boundary value problem. Computations in two dimensions are presented to illustrate the mesh independent superlinear convergence for convection-diffusion equations with both types of boundary conditions. Preconditioning by the leading term plus a zeroth-order term is also investigated in the aspect of superlinear convergence through numerical computations.