On the robustness of the topological derivative for Helmholtz problems and applications

Leugering G, Novotny AA, Sokolowski J (2022)

Publication Type: Journal article

Publication year: 2022

Journal

Control and Cybernetics Polish Academy of Sciences

Book Volume: 51

Pages Range: 227-248

Journal Issue: 2

DOI: 10.2478/candc-2022-0015

Abstract

We consider Helmholtz problems in two and three dimensions. The topological sensitivity of a given cost function J(uϵ) with respect to a small hole Bϵ around a given point x0 ϵ Bϵ ⊂ ω depends on various parameters, like the frequency k chosen or certain material parameters or even the shape parameters of the hole Bϵ. These parameters are either deliberately chosen in a certain range, as, e.g., the frequencies, or are known only up to some bounds. The problem arises as to whether one can obtain a uniform design using the topological gradient. We show that for 2-d and 3-d Helmholtz problems such a robust design is achievable.

Authors with CRIS profile

Günter Leugering Lehrstuhl für Angewandte Mathematik

Involved external institutions

Ministry of Science, Technology, Innovation and Communication (MCTIC) / Ministério da Ciência, Tecnologia, Inovações e Comunicações BR Brazil (BR) Polska Akademia Nauk (PAN) / Polish Academy of Sciences PL Poland (PL)

How to cite

APA:

Leugering, G., Novotny, A.A., & Sokolowski, J. (2022). On the robustness of the topological derivative for Helmholtz problems and applications. Control and Cybernetics, 51(2), 227-248. https://dx.doi.org/10.2478/candc-2022-0015

MLA:

Leugering, Günter, Antonio André Novotny, and Jan Sokolowski. "On the robustness of the topological derivative for Helmholtz problems and applications." Control and Cybernetics 51.2 (2022): 227-248.

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