  This paper deals with the efficient numerical solution of single-phase flow
problems in fractured porous media. A monolithic multigrid method is proposed
for solving two-dimensional arbitrary fracture networks with vertical and/or
horizontal possibly intersecting fractures. The key point is to combine
two-dimensional multigrid components (smoother and inter-grid transfer
operators) in the porous matrix with their one-dimensional counterparts within
the fractures, giving rise to a mixed-dimensional multigrid method. This
combination seems to be optimal since it provides an algorithm whose
convergence matches the multigrid convergence factor for solving the Darcy
problem. Several numerical experiments are presented to demonstrate the
robustness of the monolithic mixed-dimensional multigrid method with respect to
the permeability of the fractures, the grid size and the number of fractures in
the network.
