Algebraic multigrid preconditioning for mixed elliptic-hyperbolic problems

Algebraic multigrid solvers and preconditioners are level of the art solution techniques for many types of linear systems in science and engineering. In this contribution we will compare the computational performance of different algebraic multigrid techniques as preconditioners of Krylov-solvers for coupled systems that reflect the discretisation of problems of mixed elliptic-hyperbolic type. We will report on our experience with different aggregation and cycling strategies as well as on own development and implementation improvements. Our benchmarks are cases of different size from CFD (computational fluid dynamics) applications where the pressure-correction equation is coupled to a transport equation. Very similar systems are those solved in geo-engineering applications, e.g. in oil reservoir simulations. Recently presented k-cycle methods are very efficient and can be readily modified for such linear problems