Solvers play a crucial role in many simulations determinig the complexity of the whole process. Thus solving often limits the obtainable accuracy and fast solver even are the key to simulate new challenging problems. In the lecture multigrid methods for the simulation of large porous media flow problems are discussed. Problems like heterogeneity, non-M-matrices etc. are addresseed. Further adaptivity and parallelism is discussed. The software system UG is presented which is based on these strategies. In several application cases the efficiency of the selected approach is shown.
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