Dr. Stephan Schmidt, Uni Würzburg
Large Scale Geometric Inverse Problems and High Performance Computing
The primary concern of the presentation is geometric inverse problems governed by hyperbolic partial differential equations, meaning we are interested in reconstructing geometric objects such that they reproduce a measured echo of a scanning wave. There are a wide applications for problems of this type, including CFD, computational acoustics, Electrodynamics and mathematical imaging. We also study non-smooth problems that arise naturally when objects with kinks are to be reconstructed. To this end, we consider using Fenchel Duality and Raviart–Thomas spaces for Total Variation denoising of surfaces. The presentation concludes with numerical examples where FEM solvers are interfaced with 3D scanners to conduct denoising of real world objects and novel edge preserving mesh denoising techniques.