Volume 26, 2020
|Number of page(s)||20|
|Published online||10 December 2020|
A simplified derivation technique of topological derivatives for quasi-linear transmission problems
2 TU Wien, Wiedner Hauptstr. 8-10, 1040 Vienna, Austria.
* Corresponding author: firstname.lastname@example.org
Accepted: 7 June 2020
In this paper we perform the rigorous derivation of the topological derivative for optimization problems constrained by a class of quasi-linear elliptic transmission problems. In the case of quasi-linear constraints, techniques using fundamental solutions of the differential operators cannot be applied to show convergence of the variation of the states. Some authors succeeded showing this convergence with the help of technical computations under additional requirements on the problem. Our main objective is to simplify and extend these previous results by using a Lagrangian framework and a projection trick. Besides these generalisations the purpose of this manuscript is to present a systematic derivation approach for topological derivatives.
Mathematics Subject Classification: 49Q10 / 49Qxx / 90C46
Key words: Topological derivative / quasi-linear problems / topology optimisation / asymptotic analysis / adjoint approach
© EDP Sciences, SMAI 2020
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