Mesh Dependence in PDE-Constrained Optimisation : An Application in Tidal Turbine Array Layouts. 1st ed. 2017

種類:

電子ブック

責任表示:

by Tobias Schwedes, David A. Ham, Simon W. Funke, Matthew D. Piggott

出版情報:

Cham : Springer International Publishing : Imprint: Springer, 2017

著者名:

• Schwedes, Tobias.
• Ham, David A.
• Funke, Simon W.
• Piggott, Matthew D.
• SpringerLink (Online service)

シリーズ名:

SpringerBriefs in Mathematics of Planet Earth, Weather, Climate, Oceans ;

ISBN:

9783319594835 [3319594834]    

注記:

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.
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 arisin

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