# 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

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topAmstutz, 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 -

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