<div class="csl-bib-body">
<div class="csl-entry">Sturm, K., Baumann, P., Mazari, I., Blauth, S., & Gangl, P. (2023, September 26). <i>A second order level-set algorithm and the topological state derivatve</i> [Keynote Presentation]. Kaiserslautern Applied and Industrial Mathematics Days – KLAIM 2023, Germany.</div>
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/189295
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dc.description.abstract
In this talk we discuss first and second order methods to solve topology optimisation problems. In the first part we review the
concept of the first/second topological derivative using the so-called first and second order topological state derivative associated with a partial differential equation. Usually the topological derivative of a cost functional is defined by a circular singular perturbation, however, also other types of topological perturbations can be defined. The topological state derivative and consequently the topological derivative depends on the shape/design variable and the shape of the singular perturbation chosen. For example, in dimension two the perturbation can be a ball or a circle, in dimension $n\ge 3$ a $n$-ball or a closed hypersurface. We show how the second order topological derivative can be used to define a second order level-set algorithm following the popular level-set algorithm of Amstutz-Andr\"a. In this algorithm the shape is described by a scalar level-set function $\psi$, the interior of the design is defined by negative values of $\psi$ and the outside by positive values of $\psi$. The evolution of $\psi$, which is topically only driven by the first order topological derivative, is proposed to evolve by an update using second order information. Finally, we present numerical experiments for the Newton-type method for some model problems and compare it to the usual gradient-type level-set algorithm.
en
dc.language.iso
en
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dc.subject
topology optimisation
en
dc.title
A second order level-set algorithm and the topological state derivatve