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Mesh Dependence in PDE-Constrained Optimisation

Part of the Mathematics of Planet Earth Book Series

DOI: 10.1007/978-3-319-59483-5

ISBN: 978-3-319-59482-8

Publisher: Springer International Publishing - Springer Journals

Jul 8, 2017

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Chapter 1Introduction to PDE-constrained optimisation

Schwedes, Tobias; Ham, David A.; Funke, Simon W.; Piggott, Matthew D.

Pages: 1 –52

[The use of computational models based on the numerical solution of partial differential equations (PDEs) to simulate physical processes is a powerful complement to physical experiments. Simulations can be undertaken to consider scenarios for which experiments are impossible, such as climate...
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Chapter 2Mesh dependence in PDE-constrained optimisation

Schwedes, Tobias; Ham, David A.; Funke, Simon W.; Piggott, Matthew D.

Pages: 53 –78

[Computationally solving an optimisation problem on Hilbert spaces requires discretisation and the application of an optimisation method to the resulting finite-dimensional problem. In this context, mesh-independent convergence of the optimisation algorithm means that, for a discretisation given...
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Chapter 3An application: Optimising the layout of tidal turbine arrays

Schwedes, Tobias; Ham, David A.; Funke, Simon W.; Piggott, Matthew D.

Pages: 79 –107

[The motivation for this application comes from the desire to generate renewable energy from the tides in the Earth’s oceans. Tides are a consequence of the gravitational attractions experienced within the Earth-Moon-Sun system. As this system evolves in time the cumulative gravitational forces...

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