Mesh Dependence in PDE-Constrained Optimisation: An Application in Tidal Turbine Array Layouts

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 th... Ausführliche Beschreibung

1. Person: Schwedes, Tobias
Weitere Körperschaften: SpringerLink (Online service)
Weitere Personen: Ham, David A. [author]; Funke, Simon W. [author]; Piggott, Matthew D. [author]
Format: E-Buch
Sprache: English
Veröffentlicht: Cham Springer International Publishing 2017, 2017
Beschreibung: VIII, 110 p. 24 illus., 21 illus. in color online resource
Ausgabe: 1st ed. 2017
Serien: SpringerBriefs in Mathematics of Planet Earth, Weather, Climate, Oceans
Schlagworte: Computational Science and Engineering
Differential equations, partial
Computer science
Environmental Science and Engineering
Calculus of Variations and Optimal Control; Optimization
Partial Differential Equations
Continuous Optimization
Mathematics of Planet Earth
Mathematics
Mathematical optimization
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100 1 |a Schwedes, Tobias 
245 0 0 |a Mesh Dependence in PDE-Constrained Optimisation  |h Elektronische Ressource  |b An Application in Tidal Turbine Array Layouts  |c by Tobias Schwedes, David A. Ham, Simon W. Funke, Matthew D. Piggott 
250 |a 1st ed. 2017 
260 |a Cham  |b Springer International Publishing  |c 2017, 2017 
300 |a VIII, 110 p. 24 illus., 21 illus. in color  |b online resource 
505 0 |a 1. Introduction -- 2. Problem formulation -- 3. Shallow water equations -- 4. Aspects of the numerical solution -- 5. Optimisation methods -- 6. Mesh independent optimisation in 1-D -- 7. Mesh-dependence for Poisson constrained problem -- Index 
653 |a Computational Science and Engineering 
653 |a Differential equations, partial 
653 |a Computer science 
653 |a Environmental Science and Engineering 
653 |a Calculus of Variations and Optimal Control; Optimization 
653 |a Partial Differential Equations 
653 |a Continuous Optimization 
653 |a Mathematics of Planet Earth 
653 |a Mathematics 
653 |a Mathematical optimization 
700 1 |a Ham, David A.  |e [author] 
700 1 |a Funke, Simon W.  |e [author] 
700 1 |a Piggott, Matthew D.  |e [author] 
710 2 |a SpringerLink (Online service) 
041 0 7 |a eng  |2 ISO 639-2 
989 |b Springer  |a Springer eBooks 2005- 
490 0 |a SpringerBriefs in Mathematics of Planet Earth, Weather, Climate, Oceans 
856 |u https://doi.org/10.1007/978-3-319-59483-5?nosfx=y  |x Verlag  |3 Volltext 
082 0 |a 519 
520 |a 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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