Stabilising aggregation AMG

When applied to linear systems arising from scalar elliptic partial differential equations, algebraic multigrid (AMG) schemes based on aggregation exhibit a mesh size dependent convergence behaviour. As the number of iterations increases with the number of unknowns in the linear system, the computational complexity of such a scheme is non-optimal. This contribution presents a stabilisation of the aggregation AMG algorithm which adds a number of subspace projection steps at different stages of the algorithm and allows for variable cycling strategies. Numerical results illustrate the advantage of the stabilised algorithm over its original formulation.