AMG (Algebraic Multi-Grid) solver proved to be one of the most efficient solvers handling linear systems from discretization of the pressure equation in IMPES and Sequential Implicit formulations. We share our experience in using it in production simulations. We also discuss how AMG solver can be used as a component in composite solvers for other formulations or in parallel algorithms.

Classical AMG (Ruge-Stuben) approach is very well suited for monotone matrices from finite volume discretizations, but cannot solve efficiently linear systems with the facility unknowns included because of the different nature of these equations. We have chosen to alleviate this problem by using the multiplicative Schwarz framework. One application of this preconditioner consists of solving the facility system to a relatively loose tolerance followed by one AMG V-cycle on the pressure system. Our experiments confirm there is no loss of efficiency due to the facility unknowns. Moreover, the same approach can be extended naturally to Adaptive Implicit (AIM) formulation with different parts of the matrix handled by different linear solvers. AMG is also very efficient when used as a sub-domain solver in the overlapping additive Schwarz domain decomposition algorithm. The straightforward generalization of the serial algorithm produced unexpected results with respect to the robustness of the algorithm. The theoretical analysis provided valuable insight on the interplay of the multiplicative and additive Schwarz methods and showed us how to reorganize the algorithm to correct the problems. We also report our new findings on the influence of the overlap size between the sub-domains on the convergence of additive Schwarz method.

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