ESAIM: Control, Optimisation and Calculus of Variations

Research Article

Numerical minimization of eigenmodes of a membrane with respect to the domain

Oudet, Édouard

Institut de Recherche Mathématique Avancée, Université Louis Pasteur, 67084 Strasbourg Cedex, France;


In this paper we introduce a numerical approach adapted to the minimization of the eigenmodes of a membrane with respect to the domain. This method is based on the combination of the Level Set method of S. Osher and J.A. Sethian with the relaxed approach. This algorithm enables both changing the topology and working on a fixed regular grid.

(Received January 15 2003)

(Revised October 10 2003)

(Online publication June 15 2004)

Key Words:

  • Shape optimization;
  • eigenvalue;
  • level set;
  • relaxation.

Mathematics Subject Classification:

  • 1991