TY  - BOOK
AU  - Schwedes,Tobias
AU  - Ham,David A.
AU  - Funke,Simon W.
AU  - Piggott,Matthew D.
ED  - SpringerLink (Online service)
TI  - Mesh Dependence in PDE-Constrained Optimisation: An Application in Tidal Turbine Array Layouts 
T2  - SpringerBriefs in Mathematics of Planet Earth, Weather, Climate, Oceans,
SN  - 9783319594835
AV  - NX180.M33 
U1  - 519 23
PY  - 2017///
CY  - Cham
PB  - Springer International Publishing, Imprint: Springer
KW  - Mathematics
KW  - Environmental sciences
KW  - Partial differential equations
KW  - Mathematical optimization
KW  - Calculus of variations
KW  - Computer mathematics
KW  - Mathematics of Planet Earth
KW  - Environmental Science and Engineering
KW  - Partial Differential Equations
KW  - Continuous Optimization
KW  - Calculus of Variations and Optimal Control; Optimization
KW  - Computational Science and Engineering
N1  - 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; Available to subscribing member institutions only. Доступно лише організаціям членам підписки
N2  - 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
UR  - https://doi.org/10.1007/978-3-319-59483-5
ER  -