Implementation and analysis of multigrid schemes with finite elements for elliptic optimal control problems

DOI10.1007/s00607-008-0024-5zbMath1162.65360OpenAlexW2002177035MaRDI QIDQ1014347

Oliver Lass, Alfio Borzì, Craig C. Douglas, Michelle Vallejos

Publication date: 27 April 2009

Published in: Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00607-008-0024-5

zbMATH Keywords

convergencenumerical experimentselliptic optimal control problemsfinite element multigrid schemesmoothing strategies

Mathematics Subject Classification ID

Optimality conditions for problems involving partial differential equations (49K20) Numerical optimization and variational techniques (65K10) Newton-type methods (49M15) Existence theories for optimal control problems involving partial differential equations (49J20)

Related Items (27)

Preconditioners for reduced saddle point systems arising in elliptic PDE-constrained optimization problems ⋮ Alternating-directional PMHSS iteration method for a class of two-by-two block linear systems ⋮ Smoothing Analysis of Two Robust Multigrid Methods for Elliptic Optimal Control Problems ⋮ A leapfrog multigrid algorithm for the optimal control of parabolic PDEs with Robin boundary conditions ⋮ Fast parameterized inexact Uzawa method for complex symmetric linear systems ⋮ MGOPT with gradient projection method for solving bilinear elliptic optimal control problems ⋮ Optimizing and improving of the C-to-R method for solving complex symmetric linear systems ⋮ Accelerated PMHSS iteration methods for complex symmetric linear systems ⋮ A relaxed block splitting preconditioner for complex symmetric indefinite linear systems ⋮ Fast multilevel solvers for a class of discrete fourth order parabolic problems ⋮ A class of accelerated parameterized inexact Uzawa algorithms for complex symmetric linear systems ⋮ A reordering-based preconditioner for elliptic PDE-constrained optimization problems with small Tikhonov parameters ⋮ Additive block diagonal preconditioning for block two-by-two linear systems of skew-Hamiltonian coefficient matrices ⋮ Efficient Preconditioner and Iterative Method for Large Complex Symmetric Linear Algebraic Systems ⋮ Convergence analysis of multigrid methods with collective point smoothers for optimal control problems ⋮ Block preconditioners for elliptic PDE-constrained optimization problems ⋮ A note on block diagonal and block triangular preconditioners for complex symmetric linear systems ⋮ Convergence of a generalized PMHSS method for a class of singular block two-by-two linear systems ⋮ MN-DPMHSS iteration method for systems of nonlinear equations with block two-by-two complex Jacobian matrices ⋮ A local Fourier convergence analysis of a multigrid method using symbolic computation ⋮ Some preconditioners for elliptic PDE-constrained optimization problems ⋮ A generalized variant of simplified HSS preconditioner for generalized saddle point problems ⋮ A new multigrid method for unconstrained parabolic optimal control problems ⋮ Preconditioning of complex linear systems from the Helmholtz equation ⋮ Optimal-Order Preconditioners for Linear Systems Arising in the Semismooth Newton Solution of a Class of Control-Constrained Problems ⋮ The generalized C-to-R method for solving complex symmetric indefinite linear systems ⋮ On SSOR iteration method for a class of block two-by-two linear systems

Uses Software

• Madpack

Cites Work

• Unnamed Item
• Fast solution of elliptic control problems
• A multigrid scheme for elliptic constrained optimal control problems
• High-order discretization and multigrid solution of elliptic nonlinear constrained optimal control problems
• Multigrid optimization methods for linear and bilinear elliptic optimal control problems
• Multigrid methods for parabolic distributed optimal control problems
• Multigrid optimization in applications
• MADPACK: A family of abstract multigrid or multilevel solutions
• On the convergence of the MG/OPT method
• Multi-Grid Algorithms with Applications to Elliptic Boundary Value Problems
• Multigrid Methods for PDE Optimization
• Multi-Level Adaptive Solutions to Boundary-Value Problems
• Numerical Optimization
• Uniform Convergence of Multigrid V-Cycle Iterations for Indefinite and Nonsymmetric Problems
• Dictionary design for text image compression with JBIG2
• Nonlinear multigrid algorithms for Bayesian optical diffusion tomography
• Accuracy and Convergence Properties of the Finite Difference Multigrid Solution of an Optimal Control Optimality System
• A multigrid approach to discretized optimization problems
• Model Problems for the Multigrid Optimization of Systems Governed by Differential Equations
• The Analysis of Multigrid Algorithms with Nonnested Spaces or Noninherited Quadratic Forms

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