Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models

DOI10.1142/S0218202520500499zbMath1471.65143arXiv1910.05883OpenAlexW3088054100MaRDI QIDQ3388774

Qingguo Hong, Maria Lymbery, Fadi Philo, Johannes Kraus

Publication date: 7 May 2021

Published in: Mathematical Models and Methods in Applied Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1910.05883

zbMATH Keywords

Biot's consolidationmultiple-network poroelasticitydouble saddle point problemsparameter-robust Uzawa method

Mathematics Subject Classification ID

Flows in porous media; filtration; seepage (76S05) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Iterative numerical methods for linear systems (65F10) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Numerical solution of discretized equations for boundary value problems involving PDEs (65N22) Preconditioners for iterative methods (65F08) PDEs on graphs and networks (ramified or polygonal spaces) (35R02)

Related Items

A reverse augmented constraint preconditioner for Lagrange multiplier methods in contact mechanics ⋮ A new practical framework for the stability analysis of perturbed saddle-point problems and applications ⋮ A modified new matrix splitting preconditioner for double saddle point problems ⋮ Uniformly well-posed hybridized discontinuous Galerkin/hybrid mixed discretizations for Biot's consolidation model ⋮ Iterative splitting schemes for a soft material poromechanics model ⋮ On parameterized block symmetric positive definite preconditioners for a class of block three-by-three saddle point problems ⋮ Parameter Robust Preconditioning by Congruence for Multiple-Network Poroelasticity ⋮ Robust approximation of generalized Biot-Brinkman problems

Uses Software

• FEniCS
• poroelasticity

Cites Work

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• A nonconforming finite element method for the Biot's consolidation model in poroelasticity
• Robust fixed stress splitting for Biot's equations in heterogeneous media
• Automated solution of differential equations by the finite element method. The FEniCS book
• Convergence of iterative coupling for coupled flow and geomechanics
• Robust multigrid method for the planar linear elasticity problems
• A robust multigrid method for discontinuous Galerkin discretizations of Stokes and linear elasticity equations
• A strongly conservative finite element method for the coupling of Stokes and Darcy flow
• Parameter-robust stability of classical three-field formulation of Biot's consolidation model
• Weakly imposed symmetry and robust preconditioners for Biot's consolidation model
• Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics
• Multigrid methods for a parameter-dependent problem in primal variables
• New stabilized discretizations for poroelasticity and the Stokes' equations
• Convergence analysis of two-grid fixed stress split iterative scheme for coupled flow and deformation in heterogeneous poroelastic media
• Robust error analysis of coupled mixed methods for Biot's consolidation model
• Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media
• Monolithic and splitting solution schemes for fully coupled quasi-static thermo-poroelasticity with nonlinear convective transport
• Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics
• Space-time finite element approximation of the Biot poroelasticity system with iterative coupling
• On the inequalities of Babuška-Aziz, Friedrichs and Horgan-Payne
• Splitting schemes with respect to physical processes for double-porosity poroelasticity problems
• Block-partitioned solvers for coupled poromechanics: a unified framework
• Preconditioning Heterogeneous $\boldsymbol{H}(\mathrm{div})$ Problems by Additive Schur Complement Approximation and Applications
• A Nonconforming High-Order Method for the Biot Problem on General Meshes
• Locking-Free Finite Element Methods for Poroelasticity
• Preconditioning discretizations of systems of partial differential equations
• Parameter-Robust Discretization and Preconditioning of Biot's Consolidation Model
• Cerebral water transport using multiple-network poroelastic theory: application to normal pressure hydrocephalus
• Theory of Elasticity and Consolidation for a Porous Anisotropic Solid
• Basic concepts in the theory of seepage of homogeneous liquids in fissured rocks [strata]
• Iterative Methods by Space Decomposition and Subspace Correction
• The method of alternating projections and the method of subspace corrections in Hilbert space
• Preconditioning in H(𝑑𝑖𝑣) and applications
• Iterative Methods for Double Saddle Point Systems
• A Mixed Finite Element Method for Nearly Incompressible Multiple-Network Poroelasticity
• Preconditioning Mixed Finite Element Saddle-point Elliptic Problems
• Mixed Finite Element Methods and Applications
• Robust Block Preconditioners for Biot’s Model
• Parameter-Robust Convergence Analysis of Fixed-Stress Split Iterative Method for Multiple-Permeability Poroelasticity Systems
• Conservative discretizations and parameter‐robust preconditioners for Biot and multiple‐network flux‐based poroelasticity models
• Nodal Auxiliary Space Preconditioning in H(curl) and H(div) Spaces
• ROBUST SUBSPACE CORRECTION METHODS FOR NEARLY SINGULAR SYSTEMS
• A sharp convergence estimate for the method of subspace corrections for singular systems of equations
• Schur complement preconditioners for multiple saddle point problems of block tridiagonal form with application to optimization problems

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