Overview
- Provides an introduction to PDE-constraint optimisation, including adjoint methods and optimisation on Hilbert spaces
- Applies mathematical insights to example problems, for instance to optimisation problems arising from tidal array layouts
- Provides numerical solutions and implementation code to these problems
- Includes supplementary material: sn.pub/extras
Part of the book series: Mathematics of Planet Earth (MPE)
Part of the book sub series: SpringerBriefs in Mathematics of Planet Earth (SBMPE-WCO)
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Table of contents (3 chapters)
Keywords
- 49K20, 65K10, 65L60, 68U20, 35L25, 46E30
- gradient-based optimisation
- mesh-independent optimisation
- Riesz's representation
- tidal farm layout
- renewable energy
- discretisation dependent optimisation
- PDE-constraint optimisation
- derivative based methods
- finite elements
- adjoint methods
- partial differential equations
About this book
This book provides an introduction to PDE-constrained optimisation using finite elements and the adjoint approach. The practical impact of the mathematical insights presented here are demonstrated using the realistic scenario of the optimal placement of marine power turbines, thereby illustrating the real-world relevance of best-practice Hilbert space aware approaches to PDE-constrained optimisation problems.
Many optimisation problems that arise in a real-world context are constrained by partial differential equations (PDEs). That is, the system whose configuration is to be optimised follows physical laws given by PDEs. This book describes general Hilbert space formulations of optimisation algorithms, thereby facilitating optimisations whose controls are functions of space. It demonstrates the importance of methods that respect the Hilbert space structure of the problem by analysing the mathematical drawbacks of failing to do so. The approaches considered are illustrated using the optimisation problem arising in tidal array layouts mentioned above.
This book will be useful to readers from engineering, computer science, mathematics and physics backgrounds interested in PDE-constrained optimisation and their real-world applications.
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Authors and Affiliations
Bibliographic Information
Book Title: Mesh Dependence in PDE-Constrained Optimisation
Book Subtitle: An Application in Tidal Turbine Array Layouts
Authors: Tobias Schwedes, David A. Ham, Simon W. Funke, Matthew D. Piggott
Series Title: Mathematics of Planet Earth
DOI: https://doi.org/10.1007/978-3-319-59483-5
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Author(s) 2017
Softcover ISBN: 978-3-319-59482-8Published: 14 July 2017
eBook ISBN: 978-3-319-59483-5Published: 07 July 2017
Series ISSN: 2524-4264
Series E-ISSN: 2524-4272
Edition Number: 1
Number of Pages: VIII, 110
Number of Illustrations: 3 b/w illustrations, 21 illustrations in colour
Topics: Mathematics of Planet Earth, Environmental Science and Engineering, Partial Differential Equations, Continuous Optimization, Calculus of Variations and Optimal Control; Optimization, Computational Science and Engineering