<abstract xmlns="http://www.w3.org/1999/xhtml">

We consider Helmholtz problems in two and three dimensions. The topological sensitivity of a given cost function <italic>J</italic>(<italic>u</italic>∈) with respect to a small hole <italic>B</italic>∈ around a given point <italic>x</italic>0 ∈ <italic>B</italic>∈ ⊂ Ω depends on various parameters, like the frequency <italic>k</italic> chosen or certain material parameters or even the shape parameters of the hole <italic>B</italic>∈. 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.
</abstract>

We consider Helmholtz problems in two and three dimensions. The topological sensitivity of a given cost function J(u∈) with respect to a small hole B∈ around a given point x0 ∈ B∈ ⊂ Ω depends on various parameters, like the frequency k chosen or certain material parameters or even the shape parameters of the hole B∈. 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.

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

Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU)

Control and Cybernetics

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

We consider Helmholtz problems in two and three dimensions. The topological sensitivity of a given cost function J(u∈) with respect to a small hole B∈ around a...

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

Published Online: Aug 12, 2022

Page range: 227 - 248

Received: Mar 01, 2022

Accepted: Jun 01, 2022

DOI: https://doi.org/10.2478/candc-2022-0015

Keywords
topological derivative, shape optimization, inverse problems, Helmholtz problem, numerical methods, complex variables

© 2022 Günter Leugering et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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

Published Online: Aug 12, 2022

Page range: 227 - 248

Received: Mar 01, 2022

Accepted: Jun 01, 2022

DOI: https://doi.org/10.2478/candc-2022-0015

Keywordstopological derivative, shape optimization, inverse problems, Helmholtz problem, numerical methods, complex variables

© 2022 Günter Leugering et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
topological derivative, shape optimization, inverse problems, Helmholtz problem, numerical methods, complex variables