Reducing complexity of algebraic multigrid by aggregation

In order to decrease computational costs and memory requirements of relatively expensive classical algebraic multigrid (AMG) methods, we investigate its combination with aggressive coarsening schemes based on the plain (non-smoothed) aggregation on a fixed number of fine levels. Equivalently, we replace the direct solver on the coarsest level of the aggregation method with an inexact classical AMG solver. In this way, we obtain an efficient preconditioner with improved setup and solution costs and, at the same time, retain the convergence behavior of the exact plain aggregation method. The numerical experiments show the relevance of the proposed combination on both academic and benchmark problems related to reservoir simulation. A reduction factor of up to 2.92 in terms of computational time is obtained with respect to the classical algebraic multigrid method on this last application.