Status of system-AMG for reservoir simulation applications

Algebraic multigrid (AMG) methods for directly solving coupled systems of partial differential equations (PDEs) have been extensively used in various types of numerical simulations in engineering. A necessary condition for its efficient applicability is the simulation process being driven by elliptic components. In reservoir simulation the pressure, described by Darcy's law, is known to drive the process and hence System-AMG should be applicable and outperform classical solvers. In the context of adaptive and fully implicit reservoir simulations, the linearization of balance equations results in linear systems of equations that can be challenging. This makes it crucial to exploit all physical information from the full system to construct a robust AMG strategy and to extend it to more complex simulations than Black-Oil. At the same time, the full set of information helps to get the best out of AMG. Just as with multigrid in general, System- AMG provides a framework for combining algorithmic modules rather than a fixed solution algorithm. The adaptation of the solution strategy to the concrete class of applications is the key to obtain the best performance. Finally, System-AMG does not only allow for choosing more efficient algorithmic strategies, but also for exploiting parallelism in an optimized way, regardless of the simulation code being parallelized or not. Because the linear solver time is typically far dominating, even serial simulators can immediately and substantially benefit from MPI parallelism.