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Tesis de Pregrado de Esteban Henríquez

Henríquez, EstebanCarreraIngeniería Civil Matemática, Universidad de Concepción
Año de Ingreso2018
Año de Egreso2022
Título de la TesisAn Unfitted Hybridizable Discontinuous Galerkin Method in Shape Optimization

Resumen de la Tesis:

Resumen de la Tesis: Shape optimization seeks to optimize the shape of a region where certain partial differential equation is posed such that a functional of its solution is minimized/maximized. In this thesis we give an introduction to shape optimization through a model problem, introducing the concepts of shape derivative for a function and perturbation of the shape for a functional, we deduce the optimality conditions for the problem, and then we will present a numerical method to seek the solution via a hybridizable discontinuous Galerkin methods on curved domains. Subsequently, we develop a rigorous treatment to analyze the well-posedness of the problems that arise from the optimality conditions, and provide an a priori error analysis for each scheme.

Director(es) de Tesis Tonatiuh Sánchez-Vizuet, Manuel Solano
Fecha de Aprobación Proyecto de Tesis2021, Diciembre 15
Fecha de Defensa de Tesis2022, Diciembre 15
Seguimiento Profesional
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Publicaciones Originadas de la Tesis (ISI)

Esteban HENRIQUEZ, Manuel SOLANO: An unfitted HDG method for a distributed optimal control problem. Journal of Computational and Applied Mathematics, vol. 441, article: 115703, (2024).

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