Martin Siebenborn

Tommy Etling, Roland Herzog, Martin Siebenborn

The identification of the interface of an inclusion in a diffusion process is considered. This task is viewed as a parameter identification problem in which the parameter space bears the structure of a shape manifold. A corresponding optimum experimental design (OED) problem is formulated in which the activation pattern of an array of sensors in space and time serves as experimental condition. The goal is to improve the estimation precision within a certain subspace of the infinite dimensional tangent space of shape variations to the manifold, and to find those shape variations of best and worst identifiability. Numerical results for the OED problem obtained by a simplicial decomposition algorithm are presented.

Volker H. Schulz, Martin Siebenborn, Kathrin Welker

The novel Riemannian view on shape optimization developed in [Schulz, FoCM, 2014] is extended to a Lagrange-Newton approach for PDE constrained shape optimization problems. The extension is based on optimization on Riemannian vector space bundles and exemplified for a simple numerical example.