Automatic Differentiation for All-at-once Systems Arising in Certain PDE-Constrained Optimization Problems

An automated framework is presented for the numerical solution of optimal control problems with PDEs as constraints, in both the stationary and instationary settings. The associated code can solve both linear and non-linear problems, and examples for incompressible flow equations are considered. The...

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Bibliographic Details
Published inarXiv.org
Main Authors Leveque, Santolo, Maddison, James R, Pearson, John W
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 30.08.2024
Subjects
Automatic control
Constraints
Flow equations
Fluid flow
High level languages
Incompressible flow
Nonlinear control
Optimal control
Partial differential equations
Preconditioning
Python
Software
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Summary:An automated framework is presented for the numerical solution of optimal control problems with PDEs as constraints, in both the stationary and instationary settings. The associated code can solve both linear and non-linear problems, and examples for incompressible flow equations are considered. The software, which is based on a Python interface to the Firedrake system, allows for a compact definition of the problem considered by providing a few lines of code in a high-level language. The software is provided with efficient iterative linear solvers for optimal control problems with PDEs as constraints. The use of advanced preconditioning techniques results in a significant speed-up of the solution process for large-scale problems. We present numerical examples of the applicability of the software on classical control problems with PDEs as constraints.
ISSN:2331-8422