Generalization of algebraic multiscale to algebraic multigrid

Algebraic multiscale (AMS) is a recent development for the construction of efficient linear solvers in reservoir simulations. It employs upscaling ideas to coarsen the respective linear system and provides a high amount of inherent parallelism. However, it has the drawback that it can so far only be applied to scalar problems, e.g., a pressure sub-problem. Moreover, AMS relies on the availability of information on the physics and the grid to construct a two-level scheme. Generalizing the AMS approach to overcome these limitations requires substantial efforts and is not straightforward. To exploit the benefits of AMS, however, we integrate its core ideas in an algebraic multigrid (AMG) method. Thus, all results and techniques from the well-established AMG are directly available in conjunction with (core ingredients of) AMS. This holds regarding multilevel usage as well as the independence of geometric and physical information. But it also holds for the System-AMG approach that allows us to consider additional thermal and mechanical unknowns.