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Theory in Singularly Perturbed Geometrical Domains

  • Antonio André Novotny
  • Jan Sokołowski
  • Antoni Żochowski
Chapter
Part of the Studies in Systems, Decision and Control book series (SSDC, volume 188)

Abstract

The topological derivative method is used for numerical solution of shape and topology optimization problems. We consider singularly perturbed geometrical domains for elliptic boundary value problems. Therefore, we admit holes or cavities in the interior or singular perturbations of boundaries. In contrast to traditional approaches for shape and topology optimization, the topological derivative has been specifically designed to deal with shape and topology optimization.

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Antonio André Novotny
    • 1
  • Jan Sokołowski
    • 2
    • 3
    • 4
  • Antoni Żochowski
    • 3
  1. 1.Coordenação de Métodos Matemáticos e ComputacionaisLaboratório Nacional de Computação Científica LNCC/MCTICPetrópolisBrazil
  2. 2.Institut Élie Cartan de Nancy, UMR 7502Université de Lorraine, CNRSVandœuvre-Lès-NancyFrance
  3. 3.Systems Research InstitutePolish Academy of SciencesWarsawPoland
  4. 4.Universidade Federal da Paraiba, Centro de informaticaJoão PessoaBrazil

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