Topological sensitivity analysis for time-dependent problems
ESAIM: Control, Optimisation and Calculus of Variations, Volume 14 (2008) no. 3, pp. 427-455.

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.

DOI: 10.1051/cocv:2007059
Classification: 49Q10,  49Q12,  35K05,  35L05
Keywords: topological sensitivity, topology optimization, parabolic equations, hyperbolic equations
     author = {Vexler, Boris and Takahashi, Tak\'eo and Amstutz, Samuel},
     title = {Topological sensitivity analysis for time-dependent problems},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {427--455},
     publisher = {EDP-Sciences},
     volume = {14},
     number = {3},
     year = {2008},
     doi = {10.1051/cocv:2007059},
     mrnumber = {2434060},
     language = {en},
     url = {}
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Vexler, Boris; Takahashi, Takéo; Amstutz, Samuel. Topological sensitivity analysis for time-dependent problems. ESAIM: Control, Optimisation and Calculus of Variations, Volume 14 (2008) no. 3, pp. 427-455. doi : 10.1051/cocv:2007059.

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