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Mesh Dependence in PDE-Constrained Optimisation [electronic resource] : An Application in Tidal Turbine Array Layouts / by Tobias Schwedes, David A. Ham, Simon W. Funke, Matthew D. Piggott.

By: Schwedes, Tobias [author.].
Contributor(s): Ham, David A [author.] | Funke, Simon W [author.] | Piggott, Matthew D [author.] | SpringerLink (Online service).
Material type: TextTextSeries: SpringerBriefs in Mathematics of Planet Earth, Weather, Climate, Oceans: Publisher: Cham : Springer International Publishing : Imprint: Springer, 2017Description: VIII, 110 p. 24 illus., 21 illus. in color. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9783319594835.Subject(s): Mathematics | Differential equations, partial | Mathematical optimization | Computer science | Mathematics of Planet Earth | Environmental Science and Engineering | Partial Differential Equations | Continuous Optimization | Calculus of Variations and Optimal Control; Optimization | Computational Science and EngineeringAdditional physical formats: Printed edition:: No title; Printed edition:: No titleDDC classification: 519 Online resources: Click here to access online
Contents:
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.
In: Springer eBooksSummary: 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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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.

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