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Mesh dependence in PDE-constrained o...

Schwedes, Tobias.

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Mesh dependence in PDE-constrained optimisation = an application in tidal turbine array layouts /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Mesh dependence in PDE-constrained optimisation/ by Tobias Schwedes ... [et al.].
Reminder of title:	an application in tidal turbine array layouts /
other author:	Schwedes, Tobias.
Published:	Cham :Springer International Publishing : : 2017.,
Description:	viii, 110 p. :ill., digital ;24 cm.
[NT 15003449]:	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.
Contained By:	Springer eBooks
Subject:	Mathematical optimization. -
Online resource:	http://dx.doi.org/10.1007/978-3-319-59483-5
ISBN:	9783319594835

Mesh dependence in PDE-constrained optimisation = an application in tidal turbine array layouts /
Mesh dependence in PDE-constrained optimisationan application in tidal turbine array layouts /[electronic resource] :by Tobias Schwedes ... [et al.]. - Cham :Springer International Publishing :2017. - viii, 110 p. :ill., digital ;24 cm. - Mathematics of planet earth. - Mathematics of planet earth..

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.

ISBN: 9783319594835

Standard No.: 10.1007/978-3-319-59483-5doiSubjects--Topical Terms:

517763
Mathematical optimization.

LC Class. No.: QA402.5

Dewey Class. No.: 519.6

Mesh dependence in PDE-constrained optimisation = an application in tidal turbine array layouts /
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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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