Superlinearly convergent PCG algorithms for some nonsymmetric elliptic systems
Journal of Computational and Applied Mathematics
A mesh independent superlinear algorithm for some nonlinear nonsymmetric elliptic systems
Computers & Mathematics with Applications
Computers & Mathematics with Applications
On Superlinear PCG Methods for FDM Discretizations of Convection-Diffusion Equations
Numerical Analysis and Its Applications
Mesh Independent Convergence Rates Via Differential Operator Pairs
Large-Scale Scientific Computing
A parallel algorithm for systems of convection-diffusion equations
NMA'06 Proceedings of the 6th international conference on Numerical methods and applications
Journal of Computational and Applied Mathematics
Milestones in the development of iterative solution methods
Journal on Image and Video Processing - Special issue on iterative signal processing in communications
On symmetric part PCG for mixed elliptic problems
LSSC'05 Proceedings of the 5th international conference on Large-Scale Scientific Computing
Reaching the superlinear convergence phase of the CG method
Journal of Computational and Applied Mathematics
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The convergence of the conjugate gradient method is studied for preconditioned linear operator equations with nonsymmetric normal operators, with focus on elliptic convection-diffusion operators in Sobolev space. Superlinear convergence is proved first for equations whose preconditioned form is a compact perturbation of the identity in a Hilbert space. Then the same convergence result is verified for elliptic convection-diffusion equations using different preconditioning operators. The convergence factor involves the eigenvalues of the corresponding operators, for which an estimate is also given. The above results enable us to verify the mesh independence of the superlinear convergence estimates for suitable finite element discretizations of the convection-diffusion problems.