LEBOULANGER, Mme Marina (2024) Méthodes de décomposition de domaine pour la résolution de problèmes inverses PRE - Research Project, ENSTA.

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Abstract

In this internship, we seek to solve parameter identification problems, which are a specific type of inverse problems, using efficient numerical methods. We consider in particular an iterative gradient descent method, where the forward and adjoint problems introduced to compute the gradient are also solved iteratively. Coupling the iterations on the inverse problem unknown, the forward problem solution and the adjoint problem solution, yields the so-called one-shot inversion methods. In addition to requiring very few iterations on the forward and adjoint problems, these methods can be even more sped up by choosing an efficient iterative solver. Therefore, we decide to solve the forward and adjoint problems by domain decomposition methods. The latter consist in decomposing the problem defined on the global domain in smaller problems on subdomains, which can be solved in parallel and using robust direct solvers. Ultimately, we study numerically in this context several versions of domain decomposition algorithms, namely preconditionned fixed-point iterations or Krylov methods, in order to compare the performance of these different strategies.

Item Type:Thesis (PRE - Research Project)
Uncontrolled Keywords:inverse problems, one-shot methods, domain decomposition methods, parameter identification
Subjects:Mathematics and Applications
ID Code:10065
Deposited By:Marina LEBOULANGER
Deposited On:02 sept. 2024 16:46
Dernière modification:02 sept. 2024 16:46

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