On an Uzawa smoother in multigrid for poroelasticity equations

DOI10.1002/nla.2074zbMath1424.76041OpenAlexW2559190064MaRDI QIDQ5271010

Carmen Rodrigo, Cornelis W. Oosterlee, Peiyao Luo, Francisco José Gaspar

Publication date: 3 July 2017

Published in: Numerical Linear Algebra with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/nla.2074

zbMATH Keywords

heterogeneitymultigrid methodlocal Fourier analysisUzawa smootherporoelastic equationsiterant recombination scheme

Mathematics Subject Classification ID

Flows in porous media; filtration; seepage (76S05) Fourier series and coefficients in several variables (42B05) Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs (65M55)

Related Items (17)

A novel block non-symmetric preconditioner for mixed-hybrid finite-element-based Darcy flow simulations ⋮ Monolithic Multigrid for a Reduced-Quadrature Discretization of Poroelasticity ⋮ A two-stage preconditioner for multiphase poromechanics in reservoir simulation ⋮ Multiscale two-stage solver for Biot's poroelasticity equations in subsurface media ⋮ Robust Block Preconditioners for Biot’s Model ⋮ Monolithic multigrid method for the coupled Stokes flow and deformable porous medium system ⋮ A partially parallel-in-time fixed-stress splitting method for Biot's consolidation model ⋮ Uzawa Smoother in Multigrid for the Coupled Porous Medium and Stokes Flow System ⋮ Robust Preconditioners for a New Stabilized Discretization of the Poroelastic Equations ⋮ Tuning Multigrid Methods with Robust Optimization and Local Fourier Analysis ⋮ Approximate inverse-based block preconditioners in poroelasticity ⋮ Efficient solvers for hybridized three-field mixed finite element coupled poromechanics ⋮ On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics ⋮ A Relaxed Physical Factorization Preconditioner for Mixed Finite Element Coupled Poromechanics ⋮ Enhanced relaxed physical factorization preconditioner for coupled poromechanics ⋮ Novel mass-based multigrid relaxation schemes for the Stokes equations ⋮ Monolithic Multigrid for a Reduced-Quadrature Discretization of Poroelasticity

Uses Software

• Wesseling
• LFA

Cites Work

• Multigrid relaxation methods for systems of saddle point type
• Block-implicit multigrid solution of Navier-Stokes equations in primitive variables
• Krylov subspace acceleration for nonlinear multigrid schemes
• A Simple and Efficient Segregated Smoother for the Discrete Stokes Equations
• Local Fourier analysis for multigrid with overlapping smoothers applied to systems of PDEs
• Theory of Elasticity and Consolidation for a Porous Anisotropic Solid
• A systematic comparison of coupled and distributive smoothing in multigrid for the poroelasticity system
• Distributive smoothers in multigrid for problems with dominating grad-div operators
• Multi-Level Adaptive Solutions to Boundary-Value Problems
• Rigorous Quantitative Analysis of Multigrid, I. Constant Coefficients Two-Level Cycle with $L_2 $-Norm
• Iterative Solution Methods

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