Kolloquien und Oberseminare Übersicht Detail

Vortragende Person/Vortragende Personen:
Professor Dr.Volker Schulz (Universität Trier)

Diese Veranstaltung ist Teil der Veranstaltungsreihe „Schwerpunktskolloquium Analysis und Numerik“.

Abstract: Manifolds as such are often envisioned as curvy shapes itself. However, in this talk, we discuss manifolds of shapes. That means that each point on this manifold is itself a shape. Although this might seem, at the rst glance, as an almost too sophisticated abstraction, we will see that this point of view provides a very convenient framework for shape optimization and is able to resolve puzzles which have been severe obstacles for the development of ecient numerical algorithms in this eld of research. The concept of shape manifolds has been introduced in dierential geometry without a focus on shape optimization and thus in a setting which requires far too much smoothness for PDE constrained shape optimization, where one has to live with Sobolev spaces. In this talk, novel results on the interplay of shape manifolds and shape optimization are presented as well as their consequences for ecient and robust shape optimization algorithms in the context of system models dened by partial dierential equations.