A taxonomy and comparison of parallel block multi-level preconditioners for the incompressible Navier-Stokes equations

DOI10.1016/j.jcp.2007.09.026zbMath1290.76023OpenAlexW2163232451WikidataQ56214809 ScholiaQ56214809MaRDI QIDQ2476858

Ray S. Tuminaro, John N. Shadid, Victoria E. Howle, Robert Shuttleworth, Howard C. Elman

Publication date: 12 March 2008

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jcp.2007.09.026

zbMATH Keywords

iterative methodsincompressible flowNavier-Stokes

Mathematics Subject Classification ID

Navier-Stokes equations for incompressible viscous fluids (76D05) Iterative numerical methods for linear systems (65F10)

Related Items (67)

Updating strategy of a domain decomposition preconditioner for parallel solution of dynamic fracture problems ⋮ Local and parallel finite element algorithms based on domain decomposition for the 2D/3D Stokes equations with damping ⋮ A novel block non-symmetric preconditioner for mixed-hybrid finite-element-based Darcy flow simulations ⋮ Immersed boundary model of aortic heart valve dynamics with physiological driving and loading conditions ⋮ Variational, stable, and self-consistent coupling of 3D electromagnetics to 1D transmission lines in the time domain ⋮ A restricted additive vanka smoother for geometric multigrid ⋮ Parallel preconditioners for monolithic solution of shear bands ⋮ A massively parallel fractional step solver for incompressible flows ⋮ Parallel preconditioners for the unsteady Navier-Stokes equations and applications to hemodynamics simulations ⋮ Monolithic Multigrid Methods for Two-Dimensional Resistive Magnetohydrodynamics ⋮ Box-relaxation based multigrid solvers for the variable viscosity Stokes problem ⋮ On the stabilization of finite volume methods with co-located variables for incompressible flow ⋮ Finite element methods for large-strain poroelasticity/chemotaxis models simulating the formation of myocardial oedema ⋮ Augmented Lagrangian preconditioner for large-scale hydrodynamic stability analysis ⋮ Facsi: a block parallel preconditioner for fluid-structure interaction in hemodynamics ⋮ A parallel two-level finite element variational multiscale method for the Navier-Stokes equations ⋮ Block-partitioned solvers for coupled poromechanics: a unified framework ⋮ The nested block preconditioning technique for the incompressible Navier-Stokes equations with emphasis on hemodynamic simulations ⋮ Efficient nonlinear solvers for nodal high-order finite elements in 3D ⋮ Algorithmically scalable block preconditioner for fully implicit shallow-water equations in CAM-SE ⋮ An energy stable immersed boundary method for deformable membrane problem with non-uniform density and viscosity ⋮ Convection linearization of energy conservative implicit method for incompressible turbulence simulations ⋮ New preconditioning techniques for the steady and unsteady buoyancy driven flow problems ⋮ Block-preconditioned Newton-Krylov solvers for fully coupled flow and geomechanics ⋮ On a fully-implicit VMS-stabilized FE formulation for low Mach number compressible resistive MHD with application to MCF ⋮ Stabilization and scalable block preconditioning for the Navier-Stokes equations ⋮ Parameterized approximate block LU preconditioners for generalized saddle point problems ⋮ Improved uniform error bounds on parareal exponential algorithm for highly oscillatory systems ⋮ Solver Composition Across the PDE/Linear Algebra Barrier ⋮ A new algebraic multigrid approach for Stokes problems ⋮ Multi space reduced basis preconditioners for parametrized Stokes equations ⋮ A parallel Oseen-linearized algorithm for the stationary Navier-Stokes equations ⋮ A parallel subgrid stabilized algorithm for incompressible flows with nonlinear slip boundary conditions ⋮ Weighted BFBT Preconditioner for Stokes Flow Problems with Highly Heterogeneous Viscosity ⋮ Convergence of Some Iterative Methods for Symmetric Saddle Point Linear Systems ⋮ A robust and efficient iterative method for hyper-elastodynamics with nested block preconditioning ⋮ Parallel defect-correction algorithms based on finite element discretization for the Navier-Stokes equations ⋮ Preconditioning a Newton-Krylov solver for all-speed melt pool flow physics ⋮ A parallel subgrid stabilized finite element method based on two-grid discretization for simulation of 2D/3D steady incompressible flows ⋮ Robust Preconditioners for a New Stabilized Discretization of the Poroelastic Equations ⋮ GMRES with embedded ensemble propagation for the efficient solution of parametric linear systems in uncertainty quantification of computational models ⋮ Algebraic Multigrid Block Triangular Preconditioning for Multidimensional Three-Temperature Radiation Diffusion Equations ⋮ Monolithic Multigrid Methods for Magnetohydrodynamics ⋮ Algebraic Multigrid Block Preconditioning for Multi-Group Radiation Diffusion Equations ⋮ Local and parallel stabilized finite element algorithms based on the lowest equal-order elements for the steady Navier-Stokes equations ⋮ Memory-usage advantageous block recursive matrix inverse ⋮ Block preconditioners for finite element discretization of incompressible flow with thermal convection ⋮ High-order accurate solution of the incompressible Navier-Stokes equations on massively parallel computers ⋮ Local and parallel finite element algorithms based on two-grid discretizations for the transient Stokes equations ⋮ Block recursive LU preconditioners for the thermally coupled incompressible inductionless MHD problem ⋮ A massively parallel solver for discrete Poisson-like problems ⋮ The Development of an Object-Oriented Parallel Block Preconditioning Framework ⋮ An accurate and efficient method for the incompressible Navier-Stokes equations using the projection method as a preconditioner ⋮ On iterative methods for the incompressible Stokes problem ⋮ SLEIPNNIR: a multiscale, particle level set method for Newtonian and non-Newtonian interface flows ⋮ An overlapping domain decomposition preconditioning method for monolithic solution of shear bands ⋮ Unified computational framework for the efficient solution of \(n\)-field coupled problems with monolithic schemes ⋮ Integrated heart -- coupling multiscale and multiphysics models for the simulation of the cardiac function ⋮ An assessment of some solvers for saddle point problems emerging from the incompressible Navier-Stokes equations ⋮ Monolithic Overlapping Schwarz Domain Decomposition Methods with GDSW Coarse Spaces for Incompressible Fluid Flow Problems ⋮ Preconditioners for Two-Phase Incompressible Navier--Stokes Flow ⋮ Teko: A Block Preconditioning Capability with Concrete Example Applications in Navier--Stokes and MHD ⋮ Block Preconditioners for Stable Mixed Nodal and Edge finite element Representations of Incompressible Resistive MHD ⋮ Low-order divergence-free approximations for the Stokes problem on Worsey-Farin and Powell-Sabin splits ⋮ A Comparison of Classical and Aggregation-Based Algebraic Multigrid Preconditioners for High-Fidelity Simulation of Wind Turbine Incompressible Flows ⋮ Direct numerical simulations of particle transport in a model estuary ⋮ A parallel finite element variational multiscale method based on fully overlapping domain decomposition for incompressible flows

Uses Software

• Trilinos
• IFISS
• Chaco

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• An analysis of the fractional step method
• Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations
• Performance and analysis of saddle point preconditioners for the discrete steady-state Navier-Stokes equations
• Parallel multigrid smoothing: Polynomial versus Gauss--Seidel
• Jacobian-free Newton-Krylov methods: a survey of approaches and applications.
• Preconditioning techniques for Newton's method for the incompressible Navier-Stokes equations
• Factorization methods for the numerical approximation of Navier-Stokes equations
• Performance of fully coupled domain decomposition preconditioners for finite element transport/reaction simulations
• Preconditioning techniques for large linear systems: A survey
• A calculation procedure for heat, mass and momentum transfer in three- dimensional parabolic flows
• A Multigrid-Preconditioned Newton--Krylov Method for the Incompressible Navier--Stokes Equations
• Numerical solution of saddle point problems
• An overview of the Trilinos project
• Least Squares Preconditioners for Stabilized Discretizations of the Navier–Stokes Equations
• Stabilized Finite Element Formulations for Incompressible Flow Computations
• Preconditioning for the Steady-State Navier--Stokes Equations with Low Viscosity
• Localization of Hopf bifurcations in fluid flow problems
• Approximate Inverse Techniques for Block-Partitioned Matrices
• A Note on Preconditioning for Indefinite Linear Systems
• A Preconditioner for Generalized Saddle Point Problems
• A Preconditioner for the Steady-State Navier--Stokes Equations
• GMRESR: a family of nested GMRES methods
• Choosing the Forcing Terms in an Inexact Newton Method
• Block Preconditioners Based on Approximate Commutators
• Efficient preconditioning of the linearized Navier-Stokes equations for incompressible flow
• Convergence of algebraic multigrid based on smoothed aggregation

This page was built for publication: A taxonomy and comparison of parallel block multi-level preconditioners for the incompressible Navier-Stokes equations