The success of multigrid methods relies on complementarity between the relaxation processs and the coarse-grid correction. Multigrid methods are usually designed based on the assumption that the error that needs to be eliminated by the coarse-grid correction possesses smoothness.

We discuss several applications of practical interest where these assumptions are violated, so standard approaches cannot be successfully applied. We describe the recently developed extension of the smoothed aggregation method, designed to identify the critical error components and to incorporate them into the coarse space design. The presented numerical experiments demonstrate that the method can be used to achieve good convergence.