A minimax method in shape and topological derivatives and homogenization: the case of Helmholtz equation

  • Mame Gor Ngom Universit\'e Alioune Diop de Bambey,\\ Ecole Doctorale des Sciences et Techniques et Sciences de la Soci\'et\'e.\
  • Ibrahima Faye Université Alioune Diop de Bambey
  • Diaraf Seck Universit\'e Cheikh Anta Diop, FASEG, Dakar (S\'en\'egal)


In this paper, we perform a rigourous version of shape and topological derivatives for optimizations problems under constraint Helmoltz problems. A shape and topological optimization problem  is formulated by introducing cost  functional. We derive first by considering the lagradian method the shape derivative of the functional. It is also proven a topological derivative  with the same approach. An application to several unconstrained shape functions arising from differential geometry are also given.

Author Biography

Ibrahima Faye, Université Alioune Diop de Bambey