Superlinear PCG Algorithms: Symmetric Part Preconditioning and Boundary Conditions

Abstract

The superlinear convergence of the preconditioned CGM is studied for nonsymmetric elliptic problems (convection-diffusion equations) with mixed boundary conditions. A mesh independent rate of superlinear convergence is given when symmetric part preconditioning is applied to the FEM discretizations of the BVP. This is the extension of a similar result of the author for Dirichlet problems. The discussion relies on suitably developed Hilbert space theory for linear operators.

Keywords:

• Conjugate gradient method
• Mesh independence
• Mixed boundary conditions
• Preconditioning
• Superlinear convergence
• Symmetric part

AMS Subject Classification:

• 65J10
• 65N12
• 65N30

ACKNOWLEDGMENT

The author was supported by the Hungarian Research Grant OTKA no. T043765 and K67819.