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.

Format:

Book

Author/Creator:

Schwedes, Tobias., Author.

Ham, David A., Author.

Funke, Simon W., Author.

Piggott, Matthew D., Author.

Series:

SpringerBriefs in Mathematics of Planet Earth, Weather, Climate, Oceans, 2509-7326

Language:

English

Subjects (All):

Mathematics.

Environmental sciences.

Differential equations, Partial.

Mathematical optimization.

Calculus of variations.

Computer science--Mathematics.

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 Engineering.

Local Subjects:

Mathematics of Planet Earth.

Environmental Science and Engineering.

Partial Differential Equations.

Continuous Optimization.

Calculus of Variations and Optimal Control; Optimization.

Computational Science and Engineering.

Physical Description:

1 online resource (118 pages) : illustrations.

Edition:

1st ed. 2017.

Place of Publication:

Cham : Springer International Publishing : Imprint: Springer, 2017.

Summary:

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:

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.

Notes:

Includes bibliographical references at the end of each chapters and index.

ISBN:

3-319-59483-4