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Mathematical methods for marine energy extraction

Abstract : The present thesis aims to contribute to the development of a theoretical framework for three problems in the context of renewable marine energy. In the first part, we propose a procedure to couple unbounded in time data assimilation methods with time-parallel algorithms. The combination between the Luenberger observer and Parareal algorithm is studied, providing a way to estimate the number of parareal iterations required to preserve the observer rate of convergence, as well as an estimation of the theoretical efficiency of the entire procedure.We then discuss the determination of a bathymetry from an optimization perspective. Imposing that wave propagation must fulfill a certain criterion associated with a cost functional, we consider a PDE-constrained optimization problem where the bathymetry plays the role of control and wave propagation is described by the Helmholtz equation. We are able to prove, under suitable assumptions, the continuity of the control-to-state mapping and the existence of an optimal solution, including also some results about solutions to Helmholtz problem and convergence in a discrete framework.This work is complemented by numerical experiments.The last part of this work is devoted to analyze the convergence of the Blade element momentum (BEM) theory, a classical method used to determine the propeller efficiency as well as its design parameters. We propose a reformulation of the method that allows to obtain conditions for existence of solutions and establish the convergence of some solving algorithms. We also study the associated optimization problem in certain contexts.
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Submitted on : Monday, May 10, 2021 - 11:07:26 AM
Last modification on : Wednesday, November 17, 2021 - 12:27:07 PM
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  • HAL Id : tel-03222315, version 1



Sebastián Reyes Riffo. Mathematical methods for marine energy extraction. Data Structures and Algorithms [cs.DS]. Université Paris sciences et lettres, 2019. English. ⟨NNT : 2019PSLED068⟩. ⟨tel-03222315⟩



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