Optimal Block Preconditioner for an Efficient Numerical Solution of the Elliptic Optimal Control Problems Using Gmres Solver
DOI10.4208/ijnam2023-1003zbMath1524.49003MaRDI QIDQ6112474
Publication date: 10 July 2023
Published in: International Journal of Numerical Analysis and Modeling (Search for Journal in Brave)
saddle point problempartial differential equations (PDEs)block preconditionersPDE-optimal control problemspreconditioned generalised minimal residual method (PGMRES)
Methods involving semicontinuity and convergence; relaxation (49J45) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Existence theories for optimal control problems involving partial differential equations (49J20) Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs (65M55) Numerical solution of discretized equations for initial value and initial-boundary value problems involving PDEs (65M22)
Cites Work
- Unnamed Item
- Unnamed Item
- Block preconditioners for elliptic PDE-constrained optimization problems
- Fast solution of elliptic control problems
- Chebyshev semi-iteration in preconditioning for problems including the mass matrix
- Some preconditioners for elliptic PDE-constrained optimization problems
- A new preconditioner for elliptic PDE-constrained optimization problems
- A new approximation of the Schur complement in preconditioners for PDE-constrained optimization
- Finite Elements and Fast Iterative Solvers
- Combination preconditioning of saddle point systems for positive definiteness
- Optimal Solvers for PDE-Constrained Optimization
- Block-triangular preconditioners for PDE-constrained optimization
- A Robust Multigrid Method for Elliptic Optimal Control Problems
- Numerical solution of saddle point problems
- Symmetric Indefinite Preconditioners for Saddle Point Problems with Applications to PDE-Constrained Optimization Problems
- Optimization with PDE Constraints
- Algorithm 866
- Combination Preconditioning and the Bramble–Pasciak$^{+}$ Preconditioner
- Multigrid Methods for PDE Optimization
- Spectral Analysis of Saddle-point Matrices from Optimization problems with Elliptic PDE Constraints
- A New Iteration and Preconditioning Method for Elliptic PDE-Constrained Optimization Problems
- Block-Symmetric and Block-Lower-Triangular Preconditioners for PDE-Constrained Optimization Problems
This page was built for publication: Optimal Block Preconditioner for an Efficient Numerical Solution of the Elliptic Optimal Control Problems Using Gmres Solver