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

For further information please visit my personal website.

For further information please visit my personal website.