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This paper deals with the efficient numerical solution of single-phase flowproblems in fractured porous media. A monolithic multigrid method is proposedfor solving two-dimensional arbitrary fracture networks with vertical and/orhorizontal possibly intersecting fractures. The key point is to combinetwo-dimensional multigrid components (smoother and inter-grid transferoperators) in the porous matrix with their one-dimensional counterparts withinthe fractures, giving rise to a mixed-dimensional multigrid method. Thiscombination seems to be optimal since it provides an algorithm whoseconvergence matches the multigrid convergence factor for solving the Darcyproblem. Several numerical experiments are presented to demonstrate therobustness of the monolithic mixed-dimensional multigrid method with respect tothe permeability of the fractures, the grid size and the number of fractures inthe network.

Monolithic mixed-dimensional multigrid methods for single-phase flow in fractured porous media