Topolopogy Optimization of Eletromagnetic Devices Based on the Topological Derivative Method

• Ano de defesa: 2024
• Autor(a) principal: Mattoso, Raquel
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: eng
• Instituição de defesa: Laboratório Nacional de Computação Científica
• Palavras-chave em Português: Nanodispositivos; Materiais; Hipertemia; Equações de Maxwell; Método derivativo topológico; CNPQ::CIENCIAS EXATAS E DA TERRA::CIENCIA DA COMPUTACAO
• Link de acesso: https://tede.lncc.br/handle/tede/397

In this work we deal with topology optimization of electromagnetic devices through the topological derivative method. The forward problems are governed by the Maxwell's equations in frequency domain. These equations describe the electromagnetic phenomenon and they are fundamental to the progress of electrical, optical and radio technologies. In particular, we consider topology optimization design of nanophotonic devices, synthesis of electromagnetic metamaterials and antennas design in hyperthermia therapy. Nanophotonic devices are built in nanometer scales and can be found in applications ranging from communications to medicine. In the context of this work, we aim to obtain nanodevices which are able to concentrate electromagnetic energy inside a target region. Synthesis of metamaterials, on the other hand, consists in constructing materials with non-natural electromagnetic properties. Finally, the antenna design problem comprises in nding the optimal electromagnetic current capable to selectively heat parts of a given biological tissue. The basic idea is to de ne a shape functional for each problem in particular, which is minimized with respect to the relevant variables of interest by using the topological derivative method. Thus, the related topological derivatives are rigorously derived. Afterward, the obtained theoretical results are used to devise a family of topology optimization algorithms. Finally, a set of numerical experiments are presented for each application we are dealing with, showing di erent features of the proposed topology optimization method of electromagnetic devices.