Géraldine Pichot: [WS] The spectral domain decomposition method GenEO as a robust preconditioner for single-phase…

Speaker
Géraldine Pichot, Inria

Abstract
The Discrete Fracture Matrix (DFM) model is a classical approach for representing fractured porous media. In this model, the rock matrix is represented as a three-dimensional domain, with fractures explicitly modeled as two-dimensional planar surfaces embedded in the surrounding porous medium. Discretization of single-phase flow in DFM models with the mixed-hybrid finite element method (MHFEM) leads to very large and ill-conditioned linear systems, requiring robust preconditioning strategies. We evaluated several preconditioners: algebraic multigrid (AMG); one-level domain decomposition (DD) methods (e.g., additive Schwarz (ASM) and restricted additive Schwarz (RAS)); and two-level DD methods equipped with coarse space operators based on spectral information, either purely algebraic or GenEO (generalized eigenvalue problem on the overlap). To enable the use of GenEO in the context of DFM flows, we propose a decomposition strategy that accounts for the mixed-dimensional geometry of DFMs and facilitates the construction of the Neumann matrices and mappings required by GenEO. All numerical experiments in this work were performed using PETSc and HPDDM, with comparison against GAMG and BoomerAMG. They demonstrate that the GenEO preconditioner consistently outperforms all other tested preconditioners, both in iteration counts and wall-clock times. In the largest benchmark case, with 697,000 fractures, 243 million degrees of freedom, and 6,825 MPI processes, GMRES preconditioned with GenEO demonstrated excellent performance, completing the simulation in less than four minutes with 51 iterations.