Mesh Dependence in PDE-Constrained Optimisation - An Application in Tidal Turbine Array Layouts (Paperback, 1st ed. 2017)

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.

General

Imprint:	Springer International Publishing AG
Country of origin:	Switzerland
Series:	Mathematics of Planet Earth
Release date:	July 2017
First published:	2017
Authors:	Tobias Schwedes • David A. Ham • Simon W. Funke • Matthew D. Piggott
Dimensions:	235 x 155mm (L x W)
Format:	Paperback
Pages:	110
Edition:	1st ed. 2017
ISBN-13:	978-3-319-59482-8
Categories:	Books > Professional & Technical > Environmental engineering & technology > General Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Differential equations Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Calculus of variations Books > Science & Mathematics > Mathematics > Optimization > General Books > Science & Mathematics > Mathematics > Applied mathematics > Mathematics for scientists & engineers
LSN:	3-319-59482-6
Barcode:	9783319594828

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