A radial basis function method for solving PDE-constrained optimization problems

DOI10.1007/s11075-012-9675-6zbMath1279.65086OpenAlexW2066859971MaRDI QIDQ383516

John W. Pearson

Publication date: 4 December 2013

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

Full work available at URL: https://ora.ox.ac.uk/objects/uuid:d8f95776-3af7-4798-b633-7d5c3338ab8a

zbMATH Keywords

collocation methodnumerical resultsPoisson's equationradial basis functionsPDE-constrained optimizationmeshfree methodPoisson control

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) Existence theories for optimal control problems involving partial differential equations (49J20) Discrete approximations in optimal control (49M25)

Related Items (8)

A numerical method based on a bilinear pseudo-spectral method to solve the convection-diffusion optimal control problems ⋮ A locking-free nonconforming FEM for optimal control problems governed by linear elasticity equations ⋮ An interval for the shape parameter in radial basis function approximation ⋮ Meshless methods for solving Dirichlet boundary optimal control problems governed by elliptic PDEs ⋮ RBF collocation and hybrid-LHI methods for Stokes systems and its application to controllability problems ⋮ A Meshfree Method for a PDE-Constrained Optimization Problem ⋮ Radial basis function methods for optimal control of the convection-diffusion equation: a numerical study ⋮ Parallel generalized Lagrange-Newton method for fully coupled solution of PDE-constrained optimization problems with bound-constraints

Uses Software

• Matlab

Cites Work

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• A new approximation of the Schur complement in preconditioners for PDE-constrained optimization
• Optimal Solvers for PDE-Constrained Optimization
• Numerical solution of saddle point problems
• Meshless Collocation: Error Estimates with Application to Dynamical Systems
• Meshless Galerkin methods using radial basis functions
• Radial basis function meshless method for the steady incompressible Navier–Stokes equations
• Calculation of Gauss Quadrature Rules

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