Detailansicht
Mesh Dependence in PDE-Constrained Optimisation
An Application in Tidal Turbine Array Layouts, Mathematics of Planet Earth - SpringerBriefs in Mathematics of Planet Earth
Schwedes, Tobias/Ham, David A/Funke, Simon W et al
ISBN/EAN: 9783319594828
Umbreit-Nr.: 2315251
Sprache:
Englisch
Umfang: viii, 110 S., 3 s/w Illustr., 21 farbige Illustr.,
Format in cm:
Einband:
kartoniertes Buch
Erschienen am 14.07.2017
Auflage: 1/2017
- Zusatztext
- 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.
- Kurztext
- Provides an introduction to PDE-constraint optimisation, including adjoint methods and optimisation on Hilbert spacesApplies mathematical insights to example problems, for instance to optimisation problems arising from tidal array layoutsProvides numerical solutions and implementation code to these problemsIncludes supplementary material: sn.pub/extras