Optimizing convergence: GMRES preconditioner for Darcy flow problem in a fracture network

We suggest using a GMRES preconditioner to speed up the convergence of Krylov subspace methods for solving linear equations with a block structure. These types of equations commonly arise in unfitted finite element discretizations of the Darcy flow problem in a fracture network. We have thoroughly examined the spectrum of the preconditioned matrix to demonstrate its effectiveness. Additionally, we have conducted numerical experiments to highlight how well the preconditioners work with flexible-GMRES when solving linear equations from benchmark test problems.