A Survey of Optimal Control Problems for PDEs

DOI10.1007/978-3-030-55347-0_32zbMath1446.65159OpenAlexW3047997383MaRDI QIDQ5119118

Owe Axelsson

Publication date: 3 September 2020

Published in: Advances in High Performance Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-030-55347-0_32

Mathematics Subject Classification ID

Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) Numerical optimization and variational techniques (65K10) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Eigenvalues, singular values, and eigenvectors (15A18) Iterative numerical methods for linear systems (65F10) Parallel numerical computation (65Y05) Existence theories for optimal control problems involving partial differential equations (49J20) Discrete approximations in optimal control (49M25) Preconditioners for iterative methods (65F08) Numerical methods for ill-posed problems for boundary value problems involving PDEs (65N20)

Uses Software

• AGMG

Cites Work

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• Comparison of preconditioned Krylov subspace iteration methods for PDE-constrained optimization problems
• A comparison of iterative methods to solve complex valued linear algebraic systems
• Algebraic multilevel preconditioning methods. I
• A note on preconditioning methods for time-periodic eddy current optimal control problems
• A robust structured preconditioner for time-harmonic parabolic optimal control problems
• Iterative system solvers for the frequency analysis of linear mechanical systems
• A new version of a preconditioning method for certain two-by-two block matrices with square blocks
• Preconditioning methods for eddy-current optimally controlled time-harmonic electromagnetic problems
• Multilevel Block Factorization Preconditioners
• GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
• Iterative Solution Methods
• A coarse–fine‐mesh stabilization for an alternating Schwarz domain decomposition method
• A Flexible Inner-Outer Preconditioned GMRES Algorithm
• Matrix Iterative Analysis

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