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In recent contributions, algebraic multigrid methods have been designed andstudied from the viewpoint of the spectral complementarity. In this note wefocus our efforts on specific applications and, more precisely, on large linearsystems arising from the approximation of weighted Laplacian with variousboundary conditions. We adapt the multigrid idea to this specific setting andwe present and critically discuss a wide numerical experimentation showing thepotentiality of the considered approach.

A Note on Algebraic Multigrid Methods for the Discrete Weighted Laplacian