Enhanced relaxed physical factorization preconditioner for coupled poromechanics

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