  In recent contributions, algebraic multigrid methods have been designed and
studied from the viewpoint of the spectral complementarity. In this note we
focus our efforts on specific applications and, more precisely, on large linear
systems arising from the approximation of weighted Laplacian with various
boundary conditions. We adapt the multigrid idea to this specific setting and
we present and critically discuss a wide numerical experimentation showing the
potentiality of the considered approach.
