Numerical realization of a fictitious domain approach used in shape optimization. Part I: Distributed controls

Jana Daňková; Jaroslav Haslinger

Applications of Mathematics (1996)

  • Volume: 41, Issue: 2, page 123-147
  • ISSN: 0862-7940

Abstract

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We deal with practical aspects of an approach to the numerical realization of optimal shape design problems, which is based on a combination of the fictitious domain method with the optimal control approach. Introducing a new control variable in the right-hand side of the state problem, the original problem is transformed into a new one, where all the calculations are performed on a fixed domain. Some model examples are presented.

How to cite

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Daňková, Jana, and Haslinger, Jaroslav. "Numerical realization of a fictitious domain approach used in shape optimization. Part I: Distributed controls." Applications of Mathematics 41.2 (1996): 123-147. <http://eudml.org/doc/32941>.

@article{Daňková1996,
abstract = {We deal with practical aspects of an approach to the numerical realization of optimal shape design problems, which is based on a combination of the fictitious domain method with the optimal control approach. Introducing a new control variable in the right-hand side of the state problem, the original problem is transformed into a new one, where all the calculations are performed on a fixed domain. Some model examples are presented.},
author = {Daňková, Jana, Haslinger, Jaroslav},
journal = {Applications of Mathematics},
keywords = {shape optimization; fictitious domain approach; optimal shape design; fictitious domain method},
language = {eng},
number = {2},
pages = {123-147},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Numerical realization of a fictitious domain approach used in shape optimization. Part I: Distributed controls},
url = {http://eudml.org/doc/32941},
volume = {41},
year = {1996},
}

TY - JOUR
AU - Daňková, Jana
AU - Haslinger, Jaroslav
TI - Numerical realization of a fictitious domain approach used in shape optimization. Part I: Distributed controls
JO - Applications of Mathematics
PY - 1996
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 41
IS - 2
SP - 123
EP - 147
AB - We deal with practical aspects of an approach to the numerical realization of optimal shape design problems, which is based on a combination of the fictitious domain method with the optimal control approach. Introducing a new control variable in the right-hand side of the state problem, the original problem is transformed into a new one, where all the calculations are performed on a fixed domain. Some model examples are presented.
LA - eng
KW - shape optimization; fictitious domain approach; optimal shape design; fictitious domain method
UR - http://eudml.org/doc/32941
ER -

References

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  5. 10.1051/m2an/1993270201571, RAIRO Modèl. Math. Anal. Numér. 27 (2) (1993), 157–182. (1993) MR1211614DOI10.1051/m2an/1993270201571
  6. 10.1051/m2an/1995290404351, Math. Modelling and Numerical Analysis (MAN) 29 (1995), no. 4, 435–450. (1995) MR1346278DOI10.1051/m2an/1995290404351
  7. Finite element approximation for optimal shape, material and topology design, Second edition, J. Wiley & Sons, New-York, 1966. (1966) MR1419500
  8. 10.1007/BF02739235, Ann. Oper. Res. 5 (1985/6), 485–500. (1985/6) MR0948031DOI10.1007/BF02739235

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