On the Development of Efficient Solvers for Real-World Coupled Hydromechanical Simulations

Linear solvers usually are the most time- and memory-demanding part of a full coupled hydromechanical simulation. The typical block structure of the linearized systems arising from a fully-implicit solution approach requires the development of specialized algorithms, ensuring both robustness and computational efficiency. In particular, the design of the preconditioner to accelerate iterative methods based on Krylov subspaces is key for the overall model effectiveness. This work introduces a unifying framework for the development of preconditioning techniques in multi-physics problems, and specifically in coupled poromechanics, with the aim to provide existing methods with a novel interpretation. Three approaches, namely explicit, implicit and reverse, are considered and compared in real-world challenging benchmarks, identifying merits and drawbacks of each strategy. The proposed framework can open the way to a systematic comparison of available preconditioning tools for coupled poromechanics and help generalize the existing methods for the introduction of additional physical processes in the simulation.