Abstract

We make a theoretical analysis of the application of the generalized hierarchical basis multigrid method to the convection-diffusion equation, discretized using the Scharfetter-Gummel discretization. Our analysis is performed for two levels of grid refinement in which we compare the effects of different interpolation factors for the coarse grid basis functions on the method. In particular, we find 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.