Novel Preconditioners for Unfitted FEM in DarcyFlow for Fractured Medium

We suggest using GMRES preconditioners to solve a saddle-point problemarising from the discretization of unfitted Finite Element Method (FEM) inDarcy ow for fractured media. These problems often occur when we use a specfic method to understand how uids move in complex situations, suchas multiple dimensions. We conducted a thorough study, examining the solutions, and found that our new way of preparing the problem makes thingswork better. Spectral analysis of the proposed preconditioners, along with numerical results, showed that our method works well, especially when combinedwith a exible-GMRES method. We applied our approach to solve problemsfrom a 2D test scenario, proving that our way is practical and useful. AMS Classification: 74Sxx, 65N06, 65N12, 65F10.