Algebraic multigrid has long been established as a practical solver for a variety of problems, particularly elliptic differential equations discretized on unstructured grids.
Classical multigrid theories, however, are often carried out under assumptions not satisfied in computational practice. We will report on the results of an ongoing joint research done together with P. Vanek, C. Heberton and N. Neuss. The research focuses on relaxing some of these assumptions and extending the multigrid theory to the cases more accurately reflecting practical environment.
Our multilevel method is of smoothed-aggregation type. Modifications of the aggregation-based coarsening algorithm and of the smoothing procedures allow us to prove a convergence result for the problems with discontinuous coefficients with the same rate as for problems having no coefficient discontinuities.
The theoretical results will be illustrated by computational experiments.