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

• Autorzy: Leugering Günter , Novotny Antonio André , Sokolowski Jan

Identyfikatory

DOI

10.2478/candc-2022-0015

• Języki publikacji: EN

Abstrakty

EN

We consider Helmholtz problems in two and three dimensions. The topological sensitivity of a given cost function J(u_ɛ) with respect to a small hole B_ɛ around a given point x_0ɛ ∈ B_ɛ ⊂ Ω depends on various parameters, like the frequency k chosen or certain material parameters or even the shape parameters of the hole B_ɛ. 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.

Słowa kluczowe

EN

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

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2022
• Tom: Vol. 51, No. 2
• Strony: 227--248
• Opis fizyczny: Bibliogr. 38 poz., rys.

Twórcy

autor

Leugering Günter

• FAU Senior Fellow of Applied Mathemathics, Department of Data Science, Friedrich-Alexander-Universität Erlangen-Nüurnberg (FAU), Cauerstrasse 11, 91058 Erlangen, Germany

autor

Novotny Antonio André

• Laboratório Nacional de Computa，cão Cientifica, LNCC/MCTI, Coordena，cão de Métodos Mathemáticos e Computacionais, Av. Getúlio Vargas 333, 25651-075 Petrópolis – RJ, Brazil

autor

Sokolowski Jan

• Systems Research Institute, Polish Academy of Sciences, Newelska 6, 01-447 Warszawa, Poland

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