Preconditioning Techniques for the Numerical Solution of Flow in Fractured Porous Media

This work deals with the efficient iterative solution of the system of equations stemming from mimetic finite difference discretization of a hybrid-dimensional mixed Darcy problem modeling flow in fractured porous media. We investigate the spectral properties of a mixed discrete formulation based on mimetic finite differences for flow in the bulk matrix and finite volumes for the fractures, and present an approximation of the factors in a set of approximate block factorization preconditioners that accelerates convergence of iterative solvers applied to the resulting discrete system. Numerical tests on significant three-dimensional cases have assessed the properties of the proposed preconditioners.

Automated summary

This work focuses on efficiently solving the system of equations derived from mimetic finite difference discretization of a hybrid-dimensional mixed Darcy problem in fractured porous media. By investigating the spectral properties and proposing an approximation of block factorization preconditioners, the convergence of iterative solvers applied to the resulting discrete system is accelerated. Numerical tests on significant three-dimensional cases confirm the effectiveness of the proposed preconditioners.