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Title (deu)
Sensitivity analysis and tailored design of minimization diagrams
Speaker / Lecturer
Antoine Laurain
University Duisburg-Essen
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. Minimization diagrams encompass a large class of diagrams of interest in the literature, such as generalized Voronoi diagrams. We develop an abstract perturbation theory in two dimensions and perform a sensitivity analysis for functions depending on sets defined through intersections of smooth sublevel sets, and formulate precise conditions to avoid singular situations. This allows us to define a general framework for solving optimization problems depending on two-dimensional minimization diagrams. The particular case of Voronoi diagrams is discussed to illustrate the general theory. A variety of numerical experiments is presented, which show that the proposed methodology allows the construction of customized Voronoi diagrams using off-the-shelf well-established optimization algorithms.
Keywords (deu)
Mathematicsmetamaterialstopology optimizationshape optimization
Subject (eng)
ÖFOS 2012 -- 1010 -- Mathematics
Type (eng)
Language
[eng]
Persistent identifier
https://phaidra.univie.ac.at/o:2041831
Date created
2023-12-11
Place of creation (eng)
ESI
Duration
37 minutes 31 seconds
Content
Details
Object type
Video
Format
video/mp4
Created
11.01.2024 11:07:29