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＜電子ブック＞
Mesh Dependence in PDE-Constrained Optimisation : An Application in Tidal Turbine Array Layouts / by Tobias Schwedes, David A. Ham, Simon W. Funke, Matthew D. Piggott
(SpringerBriefs in Mathematics of Planet Earth, Weather, Climate, Oceans. ISSN:25097334)

版	1st ed. 2017.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2017
大きさ	VIII, 110 p. 24 illus., 21 illus. in color : online resource
著者標目	*Schwedes, Tobias author Ham, David A author Funke, Simon W author Piggott, Matthew D author SpringerLink (Online service)
件　名	LCSH:Geography—Mathematics LCSH:Environment LCSH:Differential equations LCSH:Mathematical optimization LCSH:Calculus of variations LCSH:Mathematics—Data processing FREE:Mathematics of Planet Earth FREE:Environmental Sciences FREE:Differential Equations FREE:Continuous Optimization FREE:Calculus of Variations and Optimization FREE:Computational Science and Engineering
一般注記	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 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 HTTP:URL=https://doi.org/10.1007/978-3-319-59483-5

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