Electrode Reconstruction by FIB/SEM and Microstructure Modelling - Optimal experimental design for PDE

The talk consists of two distinct parts, presenting the main topics of my research interests. In the first part I present a FEM model for the detailed simulation of an
electrode microstructure used in the most performing SOFC (Solid Oxide Fuel Cells). This is a joint work together with the IWE group of Prof. Ivers-Tiff´ee at KIT (Karlsruhe Institute of Technology).

Brief description: As polarization losses within SOFC electrodes are strongly related to the material microstructure and composition, a high-resolution microstructure analysis is a sensible method to understand and improve electrode performance.
By means of a dual-beam focused ion beam/scanning electron microscope (FIB/SEM) we obtain a 3D reconstruction of a high performance LSCF-cathode. These data are the basis for the calculation of the microstructure parameters like (i) surface area, (ii) volume/porosity fraction and (iii) tortuosity.
With a detailed FEM model we can calculate the electrode performance (Area Specific Resistance ASR) from the 3D reconstruction.

In the second part of the talk I give a short introduction on optimal experimental design (OED) in the context of PDE.

Brief description: The goal of the optimal experimental design (OED) is a robust prediction of the model parameters by an appropriate choice of the design (setup) of the experiments. In the OED context a robust prediction is an estimation of the parameters with the smallest variance.
In the framework of PDE this is a complex optimization task for different reasons.
On one side, it corresponds in general to a PDE-constrained minimization of a nonlinear functional, which depends on the derivatives of the state of the simulated system. On the other side, the best performing and robust techniques
are needed to solve numerically the huge problem deriving from the discretization of the system of equations. In this talk I consider the case of finite dimensional parameter space and present a numerical approach to the optimization of the
design based on a finite element method for the solution of the state equation and the sensitivity equations needed to calculate the covariance matrix of the parameters.