| Title:
|
Numerical realization of a fictitious domain approach used in shape optimization. Part I: Distributed controls (English) |
| Author:
|
Daňková, Jana |
| Author:
|
Haslinger, Jaroslav |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
41 |
| Issue:
|
2 |
| Year:
|
1996 |
| Pages:
|
123-147 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
shape optimization |
| Keyword:
|
fictitious domain approach |
| MSC:
|
49A22 |
| MSC:
|
49D30 |
| MSC:
|
49J20 |
| MSC:
|
49M30 |
| MSC:
|
49Q10 |
| idZBL:
|
Zbl 0854.49004 |
| idMR:
|
MR1373477 |
| DOI:
|
10.21136/AM.1996.134317 |
| . |
| Date available:
|
2009-09-22T17:50:40Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134317 |
| . |
| Reference:
|
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| Reference:
|
[2] R. Glowinski, A. J. Kearsley, T. W. Pan and J. Periaux: Numerical simulation and optimal shape for viscous flow by a fictitious domain method.Int. J. for Numerical Methods in Fluids 20 (1995), 695–711. MR 1333904, 10.1002/fld.1650200803 |
| Reference:
|
[3] R. Glowinski, T. W. Pan and J. Periaux: A fictitious domain method for Dirichlet problem and applications.Comput. Methods Appl. Mech. Engrg 111 (1994), 283–303. MR 1259864, 10.1016/0045-7825(94)90135-X |
| Reference:
|
[4] J. Haslinger: Embedding/Control Approach for Solving Optimal Shape Design Problems.East-West J. Numer. Math. 1, No 2 (1993), 111–119. MR 1253630 |
| Reference:
|
[5] J. Haslinger, K.-H. Hoffmann, M. Kočvara: Control/fictitious domain method for solving optimal shape design problems.RAIRO Modèl. Math. Anal. Numér. 27 (2) (1993), 157–182. MR 1211614, 10.1051/m2an/1993270201571 |
| Reference:
|
[6] J. Haslinger and A. Klarbring: Fictitious domain/mixed finite element approach for a class of optimal shape design problems.Math. Modelling and Numerical Analysis (M$^2$AN) 29 (1995), no. 4, 435–450. MR 1346278, 10.1051/m2an/1995290404351 |
| Reference:
|
[7] J. Haslinger and P. Neittaanmäki: Finite element approximation for optimal shape, material and topology design, Second edition.J. Wiley & Sons, New-York, 1966. MR 1419500 |
| Reference:
|
[8] K. Schittkowski: A Fortran Subroutine Solving Constrained Nonlinear Programming Problems.Ann. Oper. Res. 5 (1985/6), 485–500. MR 0948031, 10.1007/BF02739235 |
| . |
