Geodesic
On the numerical solution of axisymmetric domain optimization problems
Applications of Mathematics, Tome 36 (1991) no. 4, pp. 284-304

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

MR Zbl
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.
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.
DOI : 10.21136/AM.1991.104467
Classification : 49A22, 49K20, 49M15, 49Q10, 65K10, 65N30, 65N99
Keywords: shape optimization; axisymmetric elliptic problems; finite elements; cost functionals; convergence; piecewise linear approximations; numerical examples 
Hlaváček, Ivan; Mäkinen, Raino. On the numerical solution of axisymmetric domain optimization problems. Applications of Mathematics, Tome 36 (1991) no. 4, pp. 284-304. doi: 10.21136/AM.1991.104467
@article{10_21136_AM_1991_104467,
     author = {Hlav\'a\v{c}ek, Ivan and M\"akinen, Raino},
     title = {On the numerical solution of axisymmetric domain optimization problems},
     journal = {Applications of Mathematics},
     pages = {284--304},
     year = {1991},
     volume = {36},
     number = {4},
     doi = {10.21136/AM.1991.104467},
     mrnumber = {1113952},
     zbl = {0745.65044},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.1991.104467/}
}
TY  - JOUR
AU  - Hlaváček, Ivan
AU  - Mäkinen, Raino
TI  - On the numerical solution of axisymmetric domain optimization problems
JO  - Applications of Mathematics
PY  - 1991
SP  - 284
EP  - 304
VL  - 36
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.21136/AM.1991.104467/
DO  - 10.21136/AM.1991.104467
LA  - en
ID  - 10_21136_AM_1991_104467
ER  - 
%0 Journal Article
%A Hlaváček, Ivan
%A Mäkinen, Raino
%T On the numerical solution of axisymmetric domain optimization problems
%J Applications of Mathematics
%D 1991
%P 284-304
%V 36
%N 4
%U http://geodesic.mathdoc.fr/articles/10.21136/AM.1991.104467/
%R 10.21136/AM.1991.104467
%G en
%F 10_21136_AM_1991_104467

[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 | MR

[2] R. A. Brockman: Geometric Sensitivity Analysis with Isoparametric Finite Elements. Commun. appl. numer. methods, 3 (1987), 495-499. | Zbl

[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

[5] I. Hlaváček: Domain Optimization in Axisymmetric Elliptic Boundary Value Problems by Finite Elements. Apl. Mat. 33 (1988), 213-244. | MR

[6] I. Hlaváček: Shape Optimization of Elastic Axisymmetric Bodies. Apl. Mat. 34 (1989), 225-245. | MR

[7] I. Hlaváček: Domain Optimization in 3D-axisymmetric Elliptic Problems by Dual Finite Element Method. Apl. Mat. 35 (1990), 225-236. | MR

[8] R. Mäkinen: Finite Element Design Sensitivity Analysis for Nonlinear Potential Problems. Submitted for publication in Commun. appl. numer. methods. | MR

Cité par Sources :