Domain sensitivity for singular elliptic problems: Harmonic transformation approach

  • A. Zochowski
Contributed Papers


A method for computing the sensitivities of functionals depending on the solutions of elliptic equations defined over variable domains is presented. It is based on the material derivative approach and allows the uniform treatment of both singular and nonsingular cases. The novelty consists in defining the vector field connected with the domain transformation as the solution of an auxiliary elliptic equation. Such a choice does not restrict the range of admissible goal functionals and has many advantages from the numerical point of view. It allows one also to consider singular domain variations.

Key Words

Shape optimization elliptic problems material derivatives shape derivatives singularities 


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Copyright information

© Plenum Publishing Corporation 1992

Authors and Affiliations

  • A. Zochowski
    • 1
  1. 1.Systems Research InstitutePolish Academy of SciencesWarsawPoland

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