Exame de Qualificação: Topology optimizations of eletromagnetic devives based on the topological derivative method

Orientadores:
Antônio André Novotny - Laboratório Nacional de Computação Científica - LNCC

Banca Examinadora:
Pablo Javier Blanco - Laboratório Nacional de Computação Científica - LNCC (presidente)
Frédéric Gerard C. Valentin - Laboratório Nacional de Computação Científica - LNCC
Lucas Heitzmann Gabrielli - UNICAMP

Suplentes:
Renato Portugal - Laboratório Nacional de Computação Científica - LNCC

Resumo:

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 electrica l, 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 finding the optimal electromagnetic current capable to selectively heat parts of a given biological tissue. The basic idea is to define 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 different features of the proposed topology optimization method of electromagnetic devices.