One-shot solution of a time-dependent time-periodic PDE-constrained optimization problem

DOI10.1093/imanum/drt019zbMath1303.65050OpenAlexW1986724944MaRDI QIDQ2930146

Martin Stoll

Publication date: 18 November 2014

Published in: IMA Journal of Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/a481a543ab41d535a73c7239bef6ef9da4352ec3

zbMATH Keywords

Schur complementpreconditioningfast Fourier transformNewton methodnumerical resultPDE-constrained optimizationRichardson iterationsaddle point systemssaddle point systemKrylov subspace solvertime-dependent PDE-constrained optimizationtime-periodic heat equation

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) Numerical methods for discrete and fast Fourier transforms (65T50) Existence theories for optimal control problems involving partial differential equations (49J20) Discrete approximations in optimal control (49M25) Preconditioners for iterative methods (65F08)

Related Items (12)

Optimal Dirichlet control of partial differential equations on networks ⋮ Domain decomposition in time for PDE-constrained optimization ⋮ Low-Rank Eigenvector Compression of Posterior Covariance Matrices for Linear Gaussian Inverse Problems ⋮ A preconditioner for optimal control problems, constrained by Stokes equation with a time-harmonic control ⋮ Newton--Picard Preconditioners for Time-Periodic Parabolic Optimal Control Problems ⋮ Preconditioning for Vector-Valued Cahn--Hilliard Equations ⋮ PinT Preconditioner for Forward-Backward Evolutionary Equations ⋮ On the solution of the distributed optimal control problem with time‐periodic parabolic equations ⋮ Robust preconditioning techniques for multiharmonic finite element method with application to time-periodic parabolic optimal control problems ⋮ Preconditioned iterative method for boundary value method discretizations of a parabolic optimal control problem ⋮ Diagonalization-based parallel-in-time algorithms for parabolic PDE-constrained optimization problems ⋮ Application of the Alternating Direction Method of Multipliers to Control Constrained Parabolic Optimal Control Problems and Beyond

Uses Software

• deal.ii
• ML

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