Efficient solvers for hybridized three-field mixed finite element coupled poromechanics

Abstract

We consider a mixed hybrid finite element formulation for coupled poromechanics. A stabilization strategy based on a macro-element approach is advanced to eliminate the spurious pressure modes appearing in undrained/incompressible conditions. The efficient solution of the stabilized mixed hybrid block system is addressed by developing a class of block triangular preconditioners based on a Schur-complement approximation strategy. Robustness, computational efficiency and scalability of the proposed approach are theoretically discussed and tested using challenging benchmark problems on massively parallel architectures.

Monolithic multigrid for a reduced-quadrature discretization of poroelasticity

“…A family of parameterrobust schemes is found in [32] and a general theory for the error analysis is introduced. More recently, hybridization schemes are developed in [24,44]. For a four-field formulation, with the stress tensor, fluid flux, displacement, and pore pressure as unknowns, stable discretizations are developed in [37,59].…”