A Scalable Approximate Inverse Block Preconditioner for an Incompressible Magnetohydrodynamics Model Problem

DOI10.1137/19M1255409zbMath1428.76177OpenAlexW2999924267WikidataQ126403817 ScholiaQ126403817MaRDI QIDQ5208733

Michael Wathen, Chen Greif

Publication date: 10 January 2020

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/19m1255409

zbMATH Keywords

preconditionersKrylov subspace methodsnull spaceapproximate inverseincompressible magnetohydrodynamicssaddle-point linear systems

Mathematics Subject Classification ID

Computational methods for sparse matrices (65F50) Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Iterative numerical methods for linear systems (65F10) Magnetohydrodynamics and electrohydrodynamics (76W05) Basic methods in fluid mechanics (76M99) Numerical solution of discretized equations for boundary value problems involving PDEs (65N22) Preconditioners for iterative methods (65F08)

Related Items (11)

Isogeometric analysis of the time-dependent incompressible MHD equations ⋮ A novel block non-symmetric preconditioner for mixed-hybrid finite-element-based Darcy flow simulations ⋮ An Augmented Lagrangian Preconditioner for the Magnetohydrodynamics Equations at High Reynolds and Coupling Numbers ⋮ On Non-Hermitian Positive (Semi)Definite Linear Algebraic Systems Arising from Dissipative Hamiltonian DAEs ⋮ A multilevel block preconditioner for the HDG trace system applied to incompressible resistive MHD ⋮ Structure-preserving and helicity-conserving finite element approximations and preconditioning for the Hall MHD equations ⋮ New analysis of mixed finite element methods for incompressible magnetohydrodynamics ⋮ Preconditioners for Krylov subspace methods: An overview ⋮ New analysis of mixed FEMs for dynamical incompressible magnetohydrodynamics ⋮ Chronos: A General Purpose Classical AMG Solver for High Performance Computing ⋮ Monolithic Multigrid Methods for Magnetohydrodynamics

Uses Software

• hypre
• PETSc
• FEniCS

Cites Work

• Unnamed Item
• A mixed finite element method with exactly divergence-free velocities for incompressible magnetohydrodynamics
• Automated solution of differential equations by the finite element method. The FEniCS book
• Mixed finite elements in \(\mathbb{R}^3\)
• A numerical solution of the Navier-Stokes equations using the finite element technique
• Long-term dissipativity of time-stepping algorithms for an abstract evolution equation with applications to the incompressible MHD and Navier-Stokes equations
• Mixed finite element methods for stationary incompressible magneto-hydrodynamics
• An Introduction to Magnetohydrodynamics
• A Note on Preconditioning Nonsymmetric Matrices
• Block Preconditioners for Stable Mixed Nodal and Edge finite element Representations of Incompressible Resistive MHD
• A New Approximate Block Factorization Preconditioner for Two-Dimensional Incompressible (Reduced) Resistive MHD
• Finite Elements and Fast Iterative Solvers
• Preconditioners for the discretized time-harmonic Maxwell equations in mixed form
• Mathematical Methods for the Magnetohydrodynamics of Liquid Metals
• Numerical solution of saddle point problems
• Monolithic Multigrid Methods for Two-Dimensional Resistive Magnetohydrodynamics
• A Note on Preconditioning for Indefinite Linear Systems
• Preconditioners for Mixed Finite Element Discretizations of Incompressible MHD Equations
• Finite Element Methods for Maxwell's Equations
• Parallel numerical solution of the time‐harmonic Maxwell equations in mixed form
• A Block Preconditioner for an Exact Penalty Formulation for Stationary MHD
• A Charge-Conservative Finite Element Method for Inductionless MHD Equations. Part II: A Robust Solver
• On Nonsingular Saddle-Point Systems with a Maximally Rank Deficient Leading Block
• A Flexible Inner-Outer Preconditioned GMRES Algorithm
• Nodal Auxiliary Space Preconditioning in H(curl) and H(div) Spaces

This page was built for publication: A Scalable Approximate Inverse Block Preconditioner for an Incompressible Magnetohydrodynamics Model Problem