Reducing complexity of algebraic multigrid by aggregation

A typical approach to decrease computational costs and memory requirements of classical algebraic multigrid methods is to replace a conservative coarsening algorithm and short-distance interpolation on a fixed number of fine levels by an aggressive coarsening with a long-distance interpolation. Although the quality of the resulting algebraic multigrid grid preconditioner often deteriorates in terms of convergence rates and iteration counts of the preconditioned iterative solver, the overall performance can improve substantially. We investigate here, as an alternative, a possibility to replace the classical aggressive coarsening by aggregation, which is motivated by the fact that the convergence of aggregation methods can be independent of the problem size provided that the number of levels is fixed. The relative simplicity of aggregation can lead to improved solution and setup costs. The numerical experiments show the relevance of the proposed combination on both academic and benchmark problems in reservoir simulation from oil industry