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Hlaváček, Ivan; Mäkinen, Raino

On the numerical solution of axisymmetric domain optimization problems. (English) Zbl 0745.65044

Appl. Math., Praha 36, No. 4, 284-304 (1991).
Summary: An axisymmetric second order elliptic problem with mixed boundary 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.

Cited in 7 Documents

MSC:

65K10 Numerical optimization and variational techniques
49M15 Newton-type methods
49K20 Optimality conditions for problems involving partial differential equations

Keywords:

shape optimization; finite elements; axisymmetric second order elliptic problem; cost functionals; convergence; piecewise linear approximations; numerical examples

Software:

NPSOL
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\textit{I. Hlaváček} and \textit{R. Mäkinen}, Appl. Math., Praha 36, No. 4, 284--304 (1991; Zbl 0745.65044)
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References:

[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. · Zbl 0323.90063
[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.
[5] I. Hlaváček: Domain Optimization in Axisymmetric Elliptic Boundary Value Problems by Finite Elements. Apl. Mat. 33 (1988), 213-244. · Zbl 0677.65102
[6] I. Hlaváček: Shape Optimization of Elastic Axisymmetric Bodies. Apl. Mat. 34 (1989), 225-245. · Zbl 0691.73037
[7] I. Hlaváček: Domain Optimization in 3D-axisymmetric Elliptic Problems by Dual Finite Element Method. Apl. Mat. 35 (1990), 225-236. · Zbl 0731.65091
[8] R. Mäkinen: Finite Element Design Sensitivity Analysis for Nonlinear Potential Problems. Submitted for publication in Commun. appl. numer. methods. · Zbl 0716.65097
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.