@book {25071,
title = {Mesh dependence in PDE-constrained optimisation},
series = {An Application in Tidal Turbine Array Layouts},
year = {2017},
pages = {111},
publisher = {Springer Research Brief},
organization = {Springer Research Brief},
edition = {1},
address = {Berlin / Heidelberg},
abstract = {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.},
isbn = {978-3-319-59482-8},
url = {http://www.springer.com/us/book/9783319594828},
author = {Schwedes, Tobias and David A. {Ham} and Simon W {Funke} and Matthew D. {Piggott}}
}
@misc {23582,
title = {Dolfin-adjoint: Automatic adjoint models for FEniCS},
howpublished = {The 8th International Congress on Industrial and Applied Mathematics},
year = {2015},
publisher = {The 8th International Congress on Industrial and Applied Mathematics},
address = {Beijing, China},
abstract = {Adjoint and tangent linear models form the basis of many numerical techniques, including sensitivityanalysis, optimization and stability analysis. The implementation of adjoint models for nonlinear or time-dependent models are notoriously challenging: the manual approach is time-consuming and traditionalautomatic differentiation tools lack robustness and performance.dolfin-adjoint solves this problem by automatically analyzing the high-level mathematical structureinherent in finite element methods. It raises the traditional abstraction of algorithmic differentiationfrom the level of individual floating point operations to that of whole systems of differential equations.This approach delivers a number of advantages over the previous state-of-the-art: robust hands-offautomation of adjoint model derivation, optimal computational efficiency, and native parallel support.},
author = {Simon W {Funke} and Patrick Emmet {Farrell} and David A. {Ham} and Marie E. {Rognes}}
}
@article {dolfinadjoint,
title = {Automated Derivation of the Adjoint of High-Level Transient Finite Element Programs},
journal = {SIAM Journal on Scientific Computing},
volume = {35},
number = {4},
year = {2013},
pages = {369-393},
author = {Patrick Emmet {Farrell} and David A. {Ham} and Simon W {Funke} and Marie E. {Rognes}}
}
@article {Simula.simula.2030,
title = {Automating the Solution of PDEs on the Sphere and Other Manifolds in FEniCS 1.2},
journal = {Geoscientific Model Development},
number = {6},
year = {2013},
month = {June},
pages = {2099-2119},
author = {Marie E. {Rognes} and David A. {Ham} and Cotter, Colin and McRae, Andrew}
}