Mesh Dependence in PDE-Constrained Optimisation
Springer International Publishing (Verlag)
978-3-319-59482-8 (ISBN)
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.
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.
"The book is quite an interesting supplementary read for people starting to work in the field of PDE-constrained optimal control. More experienced researchers in this field may use it as a source of ideas for explaining things while teaching about PDE-constrained optimization." (Volker H. Schulz, SIAM Review, Vol. 61 (2), 2019)
“The book is quite an interesting supplementary read for people starting to work in the field of PDE-constrained optimal control. More experienced researchers in this field may use it as a source of ideas for explaining things while teaching about PDE-constrained optimization.” (Volker H. Schulz, SIAM Review, Vol. 61 (2), 2019)
| Erscheinungsdatum | 28.07.2017 |
|---|---|
| Reihe/Serie | Mathematics of Planet Earth | SpringerBriefs in Mathematics of Planet Earth |
| Zusatzinfo | VIII, 110 p. 24 illus., 21 illus. in color. |
| Verlagsort | Cham |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Gewicht | 197 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Angewandte Mathematik |
| Schlagworte | 49K20, 65K10, 65L60, 68U20, 35L25, 46E30 • adjoint methods • Applied mathematics • Calculus of Variations • Calculus of Variations and Optimal Control • computational science and engineering • Continuous Optimization • derivative based methods • Differential calculus & equations • Differential calculus & equations • discretisation dependent optimisation • Environmental Science and Engineering • environmental science, engineering & technology • Environmental science, engineering & technology • finite elements • gradient-based optimisation • Mathematics • mathematics and statistics • Mathematics of Planet Earth • Maths for scientists • mesh-independent optimisation • .NET • .NET Collections • .NET Compact Framework • .NET Enterprise Servers • .NET Framework • .NET Mobile Information Server • .NET My Services • Optimization • Partial differential equations • PDE-constraint optimisation • renewable energy • Riesz's representation • tidal farm layout • 'Unter den Linden' (Friedhof) Reutlingen |
| ISBN-10 | 3-319-59482-6 / 3319594826 |
| ISBN-13 | 978-3-319-59482-8 / 9783319594828 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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