Preconditioning by an extended matrix technique for convection-diffusion-reaction equations

Abstract

In this paper we consider a preconditioning technique for the ill-conditioned systems arising from discretisations of nonsymmetric elliptic boundary value problems. The rectangular preconditioning matrix is constructed via the transfer operators between successive discretization levels of the initial problem. In this way we get an extended, square, singular, consistent, but mesh independent well-conditioned linear system. Numerical experiments are presented for a 2D convection-diffusion-reaction problem.

Keywords

• multilevel discretization
• spectrally equivalent matrices
• mesh independent preconditioning
• positive semidefinite systems
• CGLS algorithm