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Field name	Details
Dewey Class	519
Title	Mesh Dependence in PDE-Constrained Optimisation ([EBook]) : An Application in Tidal Turbine Array Layouts / by Tobias Schwedes, David A. Ham, Simon W. Funke, Matthew D. Piggott.
Author	Schwedes, Tobias
Added Personal Name	Ham, David A.
	Funke, Simon W.
	Piggott, Matthew D.
Other name(s)	SpringerLink (Online service)
Publication	Cham : Springer International Publishing , 2017.
Physical Details	VIII, 110 pages : 24 illus., 21 illus. in color. : online resource.
Series	Mathematics of Planet Earth
ISBN	9783319594835
Summary Note	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.:
Contents note	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.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-3-319-59483-5
Links to Related Works	Subject References: Calculus of variations . Computer mathematics . Environmental Science and Engineering . Environmental Sciences . Mathematical optimization . Mathematics . Mathematics of Planet Earth . Partial differential equations . Authors: author . Funke, Simon W. . Ham, David A. . Piggott, Matthew D. . Schwedes, Tobias . Corporate Authors: SpringerLink (Online service) . Series: Mathematics of Planet Earth . Classification: 519 . 519 (DDC 23) .

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

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