A semi-circulant preconditioner for the convection-diffusion equation

In this paper we define and analyze a semi-circulant preconditioner for the convection-diffusion equation. We derive analytical formulas for the eigenvalues and the eigenvectors of the preconditioned system of equations. We show that for mesh Péclet numbers less than 2, the rate of convergence depends only on the mesh Péclet number and the direction of the convective field and not on the spatial grid ratio or the number of unknowns. Received February 20, 1997 / Revised version received November 19, 1997