Hierarchical Domain Decomposition Methods for saturated Groundwaterflow in fractured porous Media
The focus of this thesis ist the numerical computation of flow in special geometries dominated by jumps in the flow coefficients and large differences in the scales of the main flow pathes and the surrounding materials. These characteristics result in difficulties in the numerical computation of the modelling equations. By means of groundwaterflow in fractured porous media we present a hierarchical domain decomposition method for the numerical computation of flow. Under certain assumptions this new method converges independently of the fracture width, the refinement depth and the jump in the flow coefficient. The theoretical results are confirmed by practical computations of a model problem and a fracture network. Thus for a new class of completely overlapping domain decomposition methods multigrid efficiency is shown for a class of problems, for which so far no comparably theoretically validated method existed.