Enhanced relaxed physical factorization preconditioner for coupled poromechanics & nbsp;

The relaxed physical factorization (RPF) preconditioner is a recent algorithm allowing for the e?cient and robust solution to the block linear systems arising from the three-field displacement-velocity-pressure formulation of coupled poromechanics. For its application, however, it is necessary to invert blocks with the algebraic form (C) over dot= (C+ beta FFT), where C is a symmetric positive definite matrix , FFT a rank-deficient term , and & nbsp; beta a real non-negative coe?cient. The inversion of (C) over cap performed in an inexact way, can become unstable for large values of beta, as it usually occurs at some stages of a full poromechanical simulation. In this work, we propose a family of algebraic techniques to stabilize the inexact solve with (C) over cap. This strateg y can prove usef u l in other problems as wel l where such an issue might arise, such as augmented Lagrangian preconditioning techniques for Navier-Stokes or incompressible elasticity. First, we introduce an iterative scheme obtained by a natural splitting of matrix (C) over cap. Second, we develop a technique based on the use of a proper projection operator annihilating the near-kernel modes of (C) over cap. Both approaches give rise to a novel class of preconditioners denoted as Enhanced RPF (ERPF). Effectiveness and robustness of the proposed algorithms ar e demonstrated in both theoretical benchmarks and real-world large-size applications, outperforming the native RPF preconditioner.