Previous |  Up |  Next


shape optimization; axisymmetric elliptic problems; finite elements; cost functionals; convergence; piecewise linear approximations; numerical examples
An axisymmetric second order elliptic problem with mixed boundarz conditions is considered. A part of the boundary has to be found so as to minimize one of four types of cost functionals. The numerical realization is presented in detail. The convergence of piecewise linear approximations is proved. Several numerical examples are given.
[1] D. Begis R. Glowinski: Application de la méthode des éléments finis à l'approximation d'un problème de domaine optimal. Appl. Math. & Optim. 2 (1975), 130-169. DOI 10.1007/BF01447854 | MR 0443372
[2] R. A. Brockman: Geometric Sensitivity Analysis with Isoparametric Finite Elements. Commun. appl. numer. methods, 3 (1987), 495-499. Zbl 0623.73081
[3] P. E. Gill. W. Murray M. A. Saunders M. H. Wright: User's Guide for NPSOL. Technical Report SOL 84-7, Stanford University (1984).
[4] I. Hlaváček: Optimization of the Shape of Axisymmetric Shells. Apl. Mat. 28 (1983), 269-294. MR 0710176
[5] I. Hlaváček: Domain Optimization in Axisymmetric Elliptic Boundary Value Problems by Finite Elements. Apl. Mat. 33 (1988), 213-244. MR 0944785
[6] I. Hlaváček: Shape Optimization of Elastic Axisymmetric Bodies. Apl. Mat. 34 (1989), 225-245. MR 0996898
[7] I. Hlaváček: Domain Optimization in 3D-axisymmetric Elliptic Problems by Dual Finite Element Method. Apl. Mat. 35 (1990), 225-236. MR 1052744
[8] R. Mäkinen: Finite Element Design Sensitivity Analysis for Nonlinear Potential Problems. Submitted for publication in Commun. appl. numer. methods. MR 1062294
Partner of
EuDML logo