Topological sensitivity analysis for time-dependent problems

Samuel Amstutz; Takéo Takahashi; Boris Vexler

ESAIM: Control, Optimisation and Calculus of Variations (2007)

  • Volume: 14, Issue: 3, page 427-455
  • ISSN: 1292-8119

Abstract

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The topological sensitivity analysis consists in studying the behavior of a given shape functional when the topology of the domain is perturbed, typically by the nucleation of a small hole. This notion forms the basic ingredient of different topology optimization/reconstruction algorithms. From the theoretical viewpoint, the expression of the topological sensitivity is well-established in many situations where the governing p.d.e. system is of elliptic type. This paper focuses on the derivation of such formulas for parabolic and hyperbolic problems. Different kinds of cost functionals are considered.

How to cite

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Amstutz, Samuel, Takahashi, Takéo, and Vexler, Boris. "Topological sensitivity analysis for time-dependent problems." ESAIM: Control, Optimisation and Calculus of Variations 14.3 (2007): 427-455. <http://eudml.org/doc/90877>.

@article{Amstutz2007,
abstract = { The topological sensitivity analysis consists in studying the behavior of a given shape functional when the topology of the domain is perturbed, typically by the nucleation of a small hole. This notion forms the basic ingredient of different topology optimization/reconstruction algorithms. From the theoretical viewpoint, the expression of the topological sensitivity is well-established in many situations where the governing p.d.e. system is of elliptic type. This paper focuses on the derivation of such formulas for parabolic and hyperbolic problems. Different kinds of cost functionals are considered. },
author = {Amstutz, Samuel, Takahashi, Takéo, Vexler, Boris},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Topological sensitivity; topology optimization; parabolic equations; hyperbolic equations; topological sensitivity},
language = {eng},
month = {11},
number = {3},
pages = {427-455},
publisher = {EDP Sciences},
title = {Topological sensitivity analysis for time-dependent problems},
url = {http://eudml.org/doc/90877},
volume = {14},
year = {2007},
}

TY - JOUR
AU - Amstutz, Samuel
AU - Takahashi, Takéo
AU - Vexler, Boris
TI - Topological sensitivity analysis for time-dependent problems
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2007/11//
PB - EDP Sciences
VL - 14
IS - 3
SP - 427
EP - 455
AB - The topological sensitivity analysis consists in studying the behavior of a given shape functional when the topology of the domain is perturbed, typically by the nucleation of a small hole. This notion forms the basic ingredient of different topology optimization/reconstruction algorithms. From the theoretical viewpoint, the expression of the topological sensitivity is well-established in many situations where the governing p.d.e. system is of elliptic type. This paper focuses on the derivation of such formulas for parabolic and hyperbolic problems. Different kinds of cost functionals are considered.
LA - eng
KW - Topological sensitivity; topology optimization; parabolic equations; hyperbolic equations; topological sensitivity
UR - http://eudml.org/doc/90877
ER -

References

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