Abstract
The techniques of the calculus of variation and of optimization proved to be successful for several optimal shape design problems however these remain expensive both in the qualification of the engineers required to understand the method and in computing time. However it seems difficult to do without such techniques for 3-dimensional optimization problems. The field is well studied from the mathematical point of view but still in its beginnings from the industrial implementation side.
This is a preview of subscription content, log in via an institution.
Preview
Unable to display preview. Download preview PDF.
References
F. ANGRAND: Méthodes numériques pour la conception optimale en aérodynamique, 3 cycle thesis, University of Paris 6, June 1980.
D. BEGIS, R. GLOWINSKI: Application de la méthode des éléments finis à l'approximation d'un domaine optimal. Appl. Math. and Opt. 2 no 2 (1975).
J. CEA, A. GIAN, J. MICHEL: Quelques résultats sur l'identification de domaine. Calcolo III–IV (1973).
G. CHAVENT: Analyse fonctionnelle et identification de coefficients répartis. Thèse d'Etat, University of Paris 6 (1971).
D. CHESNAY: On the existence of a solution in a domain identification problem, J. of Math. Anal. and Appl. 52, 189–289 (1975).
C. CRYER: On the approximate solution of free boundary problems, J. Assoc. Comp. Mach. (1970), pp. 397–411.
A. DERVIEUX: Résolution de Problèmes à frontières libres, University of Paris 6 Thèse d'Etat, June 1981.
H. KAWARADA: Numerical methods for free surface problems by means of penalty. Lecture notes in Math. Springer 704 (1979).
J.L. LIONS: Optimal Control of Systems governed by partial differential equations North Holland (1970).
A. MARROCCO, O. PIRONNEAU: Optimum design with Lagrangian finite elements. Comp. Meth. in Appl. Mech. and Eng. 15 (1978) pp. 277–308.
Ph. MORICE: Une méthode d'optimisation de forme de domaine. Proc. IFIP-IRIA, Versailles (1974) Springer, pp. 454–467.
F. MURAT, J. SIMON. Sur le contrôle par un domaine géométrique. University of Paris 6, Doct. Thesis (1977).
F. MURAT, G. CIORANESCU: to appear.
O. PIRONNEAU, D. KATZ: Optimal swimming of flagellated micro-organism. J. Fluid. Mech. 66 (1974), pp. 391–415.
E. POLAK: Computational method in optimization. Academic Press (1971).
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1982 Springer-Verlag
About this paper
Cite this paper
Pironneau, O. (1982). Optimal shape design for elliptic systems. In: Drenick, R.F., Kozin, F. (eds) System Modeling and Optimization. Lecture Notes in Control and Information Sciences, vol 38. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0006123
Download citation
DOI: https://doi.org/10.1007/BFb0006123
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-11691-2
Online ISBN: 978-3-540-39459-4
eBook Packages: Springer Book Archive