Read While You Wait - Get immediate ebook access, if available*, when you order a print book

SpringerBriefs in Mathematics of Planet Earth Mathematics of Planet Earth Collection

Mesh Dependence in PDE-Constrained Optimisation

An Application in Tidal Turbine Array Layouts

Authors: Schwedes, T., Ham, D.A., Funke, S.W., Piggott, M.D.

Free Preview
  • 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
see more benefits

Buy this book

eBook $54.99
price for USA in USD
  • ISBN 978-3-319-59483-5
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $69.99
price for USA in USD
  • ISBN 978-3-319-59482-8
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually dispatched within 3 to 5 business days.
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.

Reviews

“The book is quite an interesting supplementary read for people starting to work in the field of PDE-constrained optimal control. More experienced researchers in this field may use it as a source of ideas for explaining things while teaching about PDE-constrained optimization.” (Volker H. Schulz, SIAM Review, Vol. 61 (2), 2019)

Table of contents (3 chapters)

Table of contents (3 chapters)

Buy this book

eBook $54.99
price for USA in USD
  • ISBN 978-3-319-59483-5
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $69.99
price for USA in USD
  • ISBN 978-3-319-59482-8
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually dispatched within 3 to 5 business days.
Loading...

Recommended for you

Loading...

Bibliographic Information

Bibliographic Information
Book Title
Mesh Dependence in PDE-Constrained Optimisation
Book Subtitle
An Application in Tidal Turbine Array Layouts
Authors
Series Title
SpringerBriefs in Mathematics of Planet Earth
Copyright
2017
Publisher
Springer International Publishing
Copyright Holder
The Author(s)
eBook ISBN
978-3-319-59483-5
DOI
10.1007/978-3-319-59483-5
Softcover ISBN
978-3-319-59482-8
Series ISSN
2509-7326
Edition Number
1
Number of Pages
VIII, 110
Number of Illustrations
3 b/w illustrations, 21 illustrations in colour
Topics

*immediately available upon purchase as print book shipments may be delayed due to the COVID-19 crisis. ebook access is temporary and does not include ownership of the ebook. Only valid for books with an ebook version. Springer Reference Works and instructor copies are not included.