Preconditioners for Mixed Finite Element Discretizations of Incompressible MHD Equations

DOI10.1137/16M1098991MaRDI QIDQ4600001

Chen Greif, Dominik Schötzau, Michael Wathen

Publication date: 5 January 2018

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

zbMATH Keywords

mixed finite element methodsSchur complementpreconditionersKrylov subspace methodsincompressible magnetohydrodynamicssaddle-point linear systems

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Finite element methods applied to problems in solid mechanics (74S05) Iterative numerical methods for linear systems (65F10) Numerical solution of discretized equations for boundary value problems involving PDEs (65N22) Preconditioners for iterative methods (65F08)

Related Items (14)

Isogeometric analysis of the time-dependent incompressible MHD equations ⋮ Efficient numerical methods for gas network modeling and simulation ⋮ 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 ⋮ A multilevel block preconditioner for the HDG trace system applied to incompressible resistive MHD ⋮ New analysis of mixed finite element methods for incompressible magnetohydrodynamics ⋮ Monolithic multigrid for implicit Runge-Kutta discretizations of incompressible fluid flow ⋮ New analysis of mixed FEMs for dynamical incompressible magnetohydrodynamics ⋮ A coercive mixed formulation for the generalized Maxwell problem ⋮ Algebraic Multigrid Block Triangular Preconditioning for Multidimensional Three-Temperature Radiation Diffusion Equations ⋮ Monolithic Multigrid Methods for Magnetohydrodynamics ⋮ Conjugate gradient for nonsingular saddle-point systems with a maximally rank-deficient leading block ⋮ A Scalable Approximate Inverse Block Preconditioner for an Incompressible Magnetohydrodynamics Model Problem ⋮ A Charge-Conservative Finite Element Method for Inductionless MHD Equations. Part II: A Robust Solver

Uses Software

• hypre
• PETSc
• FEniCS

Cites Work

• Unnamed Item
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• Mixed finite element methods for stationary incompressible magneto-hydrodynamics
• The auxiliary space method and optimal multigrid preconditioning techniques for unstructured grids
• Finite Elements and Fast Iterative Solvers
• On the Existence, Uniqueness, and Finite Element Approximation of Solutions of the Equations of Stationary, Incompressible Magnetohydrodynamics
• Preconditioners for the discretized time-harmonic Maxwell equations in mixed form
• Mathematical Methods for the Magnetohydrodynamics of Liquid Metals
• Parallel Auxiliary Space AMG for H(Curl) Problems
• A Note on Preconditioning for Indefinite Linear Systems
• 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
• Nodal Auxiliary Space Preconditioning in H(curl) and H(div) Spaces

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