Implementation strategies for block recursive factorizations

Recent advances have shown that block recursive approximate factorizations provide among the best preconditioners for solving elasticity equations on large 3D meshes such as arising in geomechanical applications. However, to get full efficiency of these methods, a wide range of implementation strategies need be put into work. In this contribution, we attempt to survey these strategies and explain their purpose. This includes level orderings and fill-in strategies, diagonal and offdiagonal relaxation, graph perturbations, reduction techniques, W-cycles and smoothing steps.