A note on algebraic multigrid methods for the discrete weighted Laplacian

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