On the numerical solution of axisymmetric domain optimization problems

Ivan Hlaváček; Raino Mäkinen

Applications of Mathematics (1991)

  • Volume: 36, Issue: 4, page 284-304
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Hlaváček, Ivan, and Mäkinen, Raino. "On the numerical solution of axisymmetric domain optimization problems." Applications of Mathematics 36.4 (1991): 284-304. <http://eudml.org/doc/15680>.

@article{Hlaváček1991,
abstract = {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.},
author = {Hlaváček, Ivan, Mäkinen, Raino},
journal = {Applications of Mathematics},
keywords = {shape optimization; axisymmetric elliptic problems; finite elements; cost functionals; convergence; piecewise linear approximations; numerical examples; shape optimization; finite elements; axisymmetric second order elliptic problem; cost functionals; convergence; piecewise linear approximations; numerical examples},
language = {eng},
number = {4},
pages = {284-304},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the numerical solution of axisymmetric domain optimization problems},
url = {http://eudml.org/doc/15680},
volume = {36},
year = {1991},
}

TY - JOUR
AU - Hlaváček, Ivan
AU - Mäkinen, Raino
TI - On the numerical solution of axisymmetric domain optimization problems
JO - Applications of Mathematics
PY - 1991
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 36
IS - 4
SP - 284
EP - 304
AB - 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.
LA - eng
KW - shape optimization; axisymmetric elliptic problems; finite elements; cost functionals; convergence; piecewise linear approximations; numerical examples; shape optimization; finite elements; axisymmetric second order elliptic problem; cost functionals; convergence; piecewise linear approximations; numerical examples
UR - http://eudml.org/doc/15680
ER -

References

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  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. (1975) MR0443372
  2. R. A. Brockman, Geometric Sensitivity Analysis with Isoparametric Finite Elements, Commun. appl. numer. methods, 3 (1987), 495-499. (1987) Zbl0623.73081
  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). (1984) 
  4. I. Hlaváček, Optimization of the Shape of Axisymmetric Shells, Apl. Mat. 28 (1983), 269-294. (1983) MR0710176
  5. I. Hlaváček, Domain Optimization in Axisymmetric Elliptic Boundary Value Problems by Finite Elements, Apl. Mat. 33 (1988), 213-244. (1988) MR0944785
  6. I. Hlaváček, Shape Optimization of Elastic Axisymmetric Bodies, Apl. Mat. 34 (1989), 225-245. (1989) MR0996898
  7. I. Hlaváček, Domain Optimization in 3D-axisymmetric Elliptic Problems by Dual Finite Element Method, Apl. Mat. 35 (1990), 225-236. (1990) MR1052744
  8. R. Mäkinen, Finite Element Design Sensitivity Analysis for Nonlinear Potential Problems, Submitted for publication in Commun. appl. numer. methods. MR1062294

Citations in EuDML Documents

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  1. Raino Mäkinen, On computer aided shape optimization
  2. Jaroslav Haslinger, Jan Stebel, Taoufik Sassi, Shape optimization for Stokes problem with threshold slip
  3. Jan Chleboun, Hybrid variational formulation of an elliptic state equation applied to an optimal shape problem
  4. Ivan Hlaváček, Michal Křížek, Weight minimization of elastic bodies weakly supporting tension. I. Domains with one curved side
  5. Ivan Hlaváček, Shape optimization of elasto-plastic axisymmetric bodies
  6. Ivan Hlaváček, Jan Chleboun, A recovered gradient method applied to smooth optimal shape problems

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