A Second Order Fixed Domain Approach to a Shape Optimization Problem

  • Henry Kasumba
  • Godwin Kakuba
  • John Mango Magero
Conference paper
Part of the Mathematics in Industry book series (MATHINDUSTRY, volume 26)


A fixed second order domain approach for solving optimal shape design problems is presented. The original optimal shape design problem is converted to an optimal control problem defined on a fixed domain. First and second order optimality conditions are derived. Numerical results are presented which demonstrate the robustness of the second order optimality conditions.



The authors appreciate the research and financial assistance extended by the Makerere University Sida phase IV Bilateral program project 316-2014, Capacity Building in Mathematics and Its Applications.


  1. 1.
    Hecht, F.: Bamg: bidimensional anisotropic mesh generator. (1998)
  2. 2.
    Ito, K., Kunisch, K., Peichl, G.: Variational approach to shape derivatives. ESAIM Control Optim. Calc. Var. 14, 517–539 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Pironneau, O.: Optimal Shape Design for Elliptic Systems. Springer, Berlin (1984)CrossRefzbMATHGoogle Scholar
  4. 4.
    Tiba, D., Neittaanmäki, P., Mäkinen, R.: A fixed domain approach in an optimal shape design problem. In: Vichnevetsky, R., Miller, J. (eds.) Proceedings of 13th IMACS World Congress on Computation and Applied Mathematics, pp. 1658–1660. Criterion Press, Dublin (1991)Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2017

Authors and Affiliations

  • Henry Kasumba
    • 1
  • Godwin Kakuba
    • 1
  • John Mango Magero
    • 1
  1. 1.Department of MathematicsMakerere UniversityKampalaUganda

Personalised recommendations