Shape optimization by means of the penalty method with extrapolation

Ivan Hlaváček

Applications of Mathematics (1994)

  • Volume: 39, Issue: 6, page 449-477
  • ISSN: 0862-7940

Abstract

top
A model shape optimal design in ℝ 2 is solved by means of the penalty method with extrapolation, which enables to obtain high order approximations of both the state function and the boundary flux, thus offering a reliable gradient for the sensitivity analysis. Convergence of the proposed method is proved for certain subsequences of approximate solutions.

How to cite

top

Hlaváček, Ivan. "Shape optimization by means of the penalty method with extrapolation." Applications of Mathematics 39.6 (1994): 449-477. <http://eudml.org/doc/32897>.

@article{Hlaváček1994,
abstract = {A model shape optimal design in $\mathbb \{R\}^2$ is solved by means of the penalty method with extrapolation, which enables to obtain high order approximations of both the state function and the boundary flux, thus offering a reliable gradient for the sensitivity analysis. Convergence of the proposed method is proved for certain subsequences of approximate solutions.},
author = {Hlaváček, Ivan},
journal = {Applications of Mathematics},
keywords = {shape optimization; penalty method; extrapolation; finite elements; finite elements; error estimates; Poisson equation; optimal shape design; cost functionals; convergence; penalty method; extrapolation},
language = {eng},
number = {6},
pages = {449-477},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Shape optimization by means of the penalty method with extrapolation},
url = {http://eudml.org/doc/32897},
volume = {39},
year = {1994},
}

TY - JOUR
AU - Hlaváček, Ivan
TI - Shape optimization by means of the penalty method with extrapolation
JO - Applications of Mathematics
PY - 1994
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 39
IS - 6
SP - 449
EP - 477
AB - A model shape optimal design in $\mathbb {R}^2$ is solved by means of the penalty method with extrapolation, which enables to obtain high order approximations of both the state function and the boundary flux, thus offering a reliable gradient for the sensitivity analysis. Convergence of the proposed method is proved for certain subsequences of approximate solutions.
LA - eng
KW - shape optimization; penalty method; extrapolation; finite elements; finite elements; error estimates; Poisson equation; optimal shape design; cost functionals; convergence; penalty method; extrapolation
UR - http://eudml.org/doc/32897
ER -

References

top
  1. 10.1090/S0025-5718-1973-0351118-5, Math. Comp. 27 (1973), 221–228. (1973) MR0351118DOI10.1090/S0025-5718-1973-0351118-5
  2. Numerical solution of partial differential equations, Preprint, March 1973, Univ. of Maryland. MR0366062
  3. Basic error estimates for elliptic problems, In: Handbook of Numer. Anal., vol. II, Finite element methods (Part 1), ed. by P.G. Ciarlet and J.L. Lions, Elsevier, (North-Holland), 1991. Zbl0875.65086MR1115237
  4. Elementary numerical analysis; an algorithmic approach, McGraw-Hill, New York, 1972. (1972) MR0202267
  5. Boundary value problems in non-smooth domains, Univ. of Maryland, Lecture Notes #19, 1980. (1980) 
  6. Singularities in boundary value problems, RMA 22, Res. Notes in Appl. Math., Masson, Paris, Springer-Verlag, Berlin, 1992. (1992) Zbl0778.93007MR1173209
  7. Design sensitivity analysis of structural systems, Academic Press, Orlando-London, 1986. (1986) MR0860040
  8. Penalty method and extrapolation for axisymmetric elliptic problems with Dirichlet boundary conditions, Apl. Mat. 35 (1990), 405–417. (1990) MR1072609
  9. Primal formulation of an elliptic equation in smooth optimal shape problems. Advances in Math. Sci. Appl., . 
  10. On the regularity of the solution of the Poisson problem on a domain with boundary locally similar to the boundary of a convex open set, Czechoslovak Math. J. 14 (1964), no. 89, 386–393.. (1964) Zbl0166.37703MR0170088
  11. 10.1007/BF01459948, Numer. Math. 23 (1974), 153–165. (1974) Zbl0272.65092MR0400742DOI10.1007/BF01459948
  12. 10.1007/BF02252082, Computing, 16 (1976), 339–347. (1976) MR0418485DOI10.1007/BF02252082
  13. 10.1090/S0025-5718-1978-0471866-0, Math. Comp. 32 (1978), 111–126. (1978) MR0471866DOI10.1090/S0025-5718-1978-0471866-0
  14. Problèmes aux limites non homogènes et applications, vol. 1, Dunod, Paris, 1968. (1968) MR0247243
  15. Les méthodes directes en théorie des équations elliptiques, Academia, Prague, 1967. (1967) MR0227584
  16. 10.1137/0710022, SIAM J. Num. Anal. 10 (1973), 229–240. (1973) MR0395263DOI10.1137/0710022

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.