In many practical engineering applications, products are designed using methods of
numerical shape optimization. These methods originate from applications in mechanical engineering,
but have been applied to a wide variety of fields of engineering such as electrical engineering, fluid
mechanics or even multiphysics applications. In most practically interesting applications, the objective
function depends on the design via the solution of a partial differential equation (PDE), thus one is
facing a problem of PDE-constrained shape optimization. In particular, many relevant problems
involve a constraint in the form of a PDE, which contains inputs or material properties that may
be unknown or subject to uncertainty. In contrast to classical optimal control problems, where the
unknown is an element of a function space, in shape optimization we are searching for the optimal
shape of a domain or subdomain. Since the set of admissible shapes does not admit a vector space
structure, different ways of sensitivity analysis and optimization have to be followed. For example,
there is a natural connection to differential geometry, since the characterization of optimal shapes and
their computation relies on geometric quantities.
The topics to be treated within this minisymposium range from more theoretical aspects such as
questions regarding distance concepts between shapes and sensitivity analysis with respect to shape
perturbations of domains over the design of (deterministic and stochastic) optimization algorithms to
the practical realization and implementation of optimization methods and its application to realistic
problems.
Mini symposium organizer:
Kathrin Welker (TU Bergakademie Freiberg)
Session 1. Room A3, Tuesday 18:00-19:30.
Chair: Tim Suchan (Helmut-Schmidt-Universität / Universität der Bundeswehr Hamburg)
Speakers:
Christine Herter (Universität Hamburg) Eigenvalue Optimization with respect to Shape-Variations in Electromagnetic Cavities
Karen Estefania Loayza Romero (Imperial College London) Multi-level Optimal Control with Neural Surrogate Models
Julien Prando (Université Grenoble Alpes) Distributionally Robust Density Optimisation with Wasserstein Distance and Applications
Session 2. Room A3, Wednesday 11:30-13:30.
Chair: Karen Estefania Loayza Romero (Imperial College London)
Speakers:
Lidiya Pryymak (TU Bergakademie Freiberg) Shape optimization on Riemannian manifolds
Matthias Schuster (Universität Trier) Second Shape Derivative for an Interface Identification Problem constrained by Nonlocal Models
Tim Suchan (Helmut-Schmidt-Universität / Universität der Bundeswehr Hamburg) Optimization of multiple shapes: from PDE constraints under uncertainty to variational inequality constraints
André-Alexander Zepernick (Freie Universität Berlin) Quasi-Monte Carlo Methods for PDEs on Randomly Moving Domains