Henrik Wyschka

Solution of p-Laplace equations and their limits with application to shape optimization on high performance computer architectures - O3

Shape optimization constrained to partial differential equations is a vivid field of research with high relevance for industrial grade applications. Recent development suggests that using a p-harmonic approach to determine descent directions yields superior results compared to classical Hilbert space methods. However, this approach requires the solution of a non-linear vector-valued p-Laplace problem including source terms in each iteration. Our research is concerned with the development of an efficient algorithm for this type of problem with large p. Especially without an iteration over p, which is indispensable for the scalability of the outer optimization. The results are then applied to the optimization of aerodynamic shapes in Euler and Navier-Stokes flows.

Further, we consider the computation of analytically admissible deformations to the underlying finite element mesh while preserving the grid quality. This is strongly connected to identifying the limit of p-harmonic descent directions and an algorithm for corresponding ∞-Laplacian problems. In this context, difficulties arise in particular from an essential change of sign in the source terms to fulfill geometric constraints during an optimization process. Connections are established with the project O2, dealing with applications to ship hulls in free surface flows.

Advisor: Prof. Dr. Winnifried Wollner
Co-Advisor: Prof. Dr. -Ing.  Thomas Rung
Consultant: Dr. Martin Siebenborn

18.-22.03.2024
GAMM Annual Meeting 2024, Magdeburg (GER): "A Trust-Region Method for p-Harmonic Shape Optimization"

11.-13.03.2024
CSE Workshop on Modeling, Simulation & Optimization of Fluid Dynamic Applications, Groß Schwansee (GER): "A Trust-Region Method for p-Harmonic Shape Optimization"

20.-25.08.2023
10th International Congress on Industrial and Applied Mathematics (ICIAM), Tokyo (JPN): "Computing p-Harmonic Descent Directions for Shape Optimization"

24.-26.07.2023
German SIAM Student Chapters Meet Algorithmic Optimization, Trier (GER): "Descent Directions in p-Harmonic Shape Optimization"

30.06.2023
GAMM Student Chapter Science Slam, Hannover (GER): "Shape Optimization for Runaways: Is 4.1 infinte?"

30.05.-03.06.2023
SIAM Conference on Optimization, Seattle (USA): "Computing p-Harmonic Descent Directions and Their Limits for Shape Optimization"

20.-22.03.2023
CSE Workshop on Computational Science and Engineering, Groß Schwansee (GER): “Computing p-Harmonic Descent Directions and Their Limits for Shape Optimization"

26.02.-03.03.2023
SIAM Conference on Computational Science and Engineering (CSE23), Amsterdam (NED): “Computing p-Harmonic Descent Directions and Their Limits for Shape Optimization" (Poster)

20.-22.03.2023

CSE Workshop on Computational Science and Engineering, Groß Schwansee (GER): “Computing p-Harmonic Descent Directions and Their Limits for Shape Optimization"

15.-19.08.2022
GAMM Annual Meeting 2022, Aachen (GER): “On Computing p-Harmonic Descent Directions and Their Limits for Shape Optimization"

21.-24.03.2022
CSE Workshop on Modeling, Simulation & Optimization of Fluid Dynamic Applications, Groß Schwansee (GER): “Towards Computing High-Order p-Harmonic Descent Directions and Their Limits in Shape Optimization”

Wyschka, H., Siebenborn, M.: "Towards Computing High-Order p-Harmonic Descent Directions and Their Limits in Shape Optimization", In: "Modeling, Simulation and Optimization of Fluid Dynamic Applications", Springer, 2023.