questions on shape reconstruction, presenting counterexamples for Robin boundary conditions or with additional unknown Lamé parameters. Using the method of fundamental solutions (MFS) we adapt a method introduced twenty years ago by Andreas Kirsch and Rainer Kress [17] (in the context of an exterior

. It would seem that some forms of bionic vision have gone the way of rocket backpacks – that is, until recently. The newest book by Andreas Kirsch with coauthor Natalia Grinberg, The Factorization Method for Inverse Problems, collects over a decade of work by Kirsch and collaborators on a simple method

to François Alouges, Xavier Antoine, Anne-Sophie Bonnet-Ben Dhia, Johannes Elschner and Andreas Kirsch for their willingness to be members of my defense committee. I am particularly grateful to Xavier Antoine and Johannes Elschner for their helpful comments and for the patience they paid to carefully read

First, I want to thank my supervisor Professor Christoph Kirsch who gave me the opportunity to work on an interesting research project and provided excellent mentoring. I also want to point out the great working environment which facilitated the writing of this thesis considerably. The software