PMHSS iteration method and preconditioners for Stokes control PDE-constrained optimization problems

DOI10.1007/s11075-020-00970-1zbMath1468.65028OpenAlexW3042900321MaRDI QIDQ2021775

Publication date: 27 April 2021

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11075-020-00970-1

zbMATH Keywords

preconditioning PDE-constrained optimization problems Hermitian/skew-Hermitian splitting Stokes control

Mathematics Subject Classification ID

Iterative numerical methods for linear systems (65F10) Flow control and optimization for incompressible viscous fluids (76D55) Preconditioners for iterative methods (65F08)

Related Items (2)

A variant of PMHSS iteration method for a class of complex symmetric indefinite linear systems ⋮ Rotated block diagonal preconditioners for Navier-Stokes control problems

Uses Software

HSL_MI20

Cites Work

A comparison of iterative methods to solve complex valued linear algebraic systems
Comparison of preconditioned Krylov subspace iteration methods for PDE-constrained optimization problems. Stokes control
A new block preconditioner for complex symmetric indefinite linear systems
On preconditioned iteration methods for complex linear systems
Restrictively preconditioned Chebyshev method for solving systems of linear equations
An improved block splitting preconditioner for complex symmetric indefinite linear systems
On parameterized inexact Uzawa methods for generalized saddle point problems
Bounds for the smallest singular value of a Jordan block with an application to eigenvalue perturbation
A variant of the HSS preconditioner for complex symmetric indefinite linear systems
A new version of a preconditioning method for certain two-by-two block matrices with square blocks
On the development of parameter-robust preconditioners and commutator arguments for solving Stokes control problems
Modified complex-symmetric and skew-Hermitian splitting iteration method for a class of complex-symmetric indefinite linear systems
A generalization of preconditioned MHSS iteration method for complex symmetric indefinite linear systems
On generalized successive overrelaxation methods for augmented linear systems
Finite Elements and Fast Iterative Solvers
Optimal Solvers for PDE-Constrained Optimization
Nonstandard Norms and Robust Estimates for Saddle Point Problems
Realistic Eigenvalue Bounds for the Galerkin Mass Matrix
Some fast 3D finite element solvers for the generalized Stokes problem
Inexact and Preconditioned Uzawa Algorithms for Saddle Point Problems
On a Chebyshev accelerated splitting iteration method with application to two‐by‐two block linear systems
Preconditioned MHSS iteration methods for a class of block two-by-two linear systems with applications to distributed control problems
Efficient Solvers for Saddle Point Problems with Applications to PDE–Constrained Optimization
The generalized C-to-R method for solving complex symmetric indefinite linear systems
HSL_MI20 : An efficient AMG preconditioner for finite element problems in 3D
On Preconditioned MHSS Real-Valued Iteration Methods for a Class of Complex Symmetric Indefinite Linear Systems

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