Numerical approximation of topological derivatives and some applications

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Title (deu)

Speaker / Lecturer

Peter Gangl

RICAM, Linz

Description (deu)

This talk was part of the Workshop on "New perspective on Shape and Topology Optimization" held at the ESI December 11 — 15, 2023. Topological derivatives represent the sensitivity of a given design-dependent cost function with respect to the insertion of small inclusions of different materials. The concept has proven useful in a large number of applications, ranging from design optimization of structures to inverse problems and applications in mathematical imaging. While closed-form formulas can be given for many relevant PDE-constrained topology optimization problems, this is not the case when the inclusion shape is non-standard or when the underlying PDE is quasilinear. We illustrate a way to numerically approximate the topological derivative also in these cases and apply this technique to the (multi-material) design optimization of electric machines and the task of corner detection in mathematical imaging.

Keywords (deu)

Mathematicsmetamaterialstopology optimizationshape optimization

Subject (eng)

ÖFOS 2012 -- 1010 -- Mathematics

Type (eng)

lecture

Language

[eng]

Persistent identifier

https://phaidra.univie.ac.at/o:2041835

Date created

2023-12-12