The generalized hierarchical basis two - levelmethod for the convection - di usion equationon a regular

We make a theoretical analysis of the application of the generalized hierarchical basis multigrid method to the convection-diiusion equation, discretized using the Scharfetter-Gummel discretization. Our analysis is performed for two levels of grid reenement in which we compare the eeects of diierent interpolation factors for the coarse grid basis functions on the method. In particular, we nd the asymptotic convergence rates for the Scharfetter-Gummel-and the ILU-factors. The ILU-factors produce convergence rates independent of the convection directions but dependent on the size of the convection vector. Numerical results illustrating these rates are given.