Research Interests of Dr F. Hettlich
- Theory and numerical approximation of the scattering of acoustic, electromagnetic, or elastic waves, in particular integral equation methods and weak formulations
- Questions on the existence and representation of domain derivatives, i.e. derivatives of solutions of partial differential equations with respect to variations of the underlying geometry
- Inverse Problems for partial differential equations, in particular uniqueness of obstacle reconstruction problems and parameter identification
- Numerical methods for nonlinear ill-posed problems, for instance establishing iterative regularization schemes
The figure shows a reconstruction (red line) of a scattering object (black dashed line) from a far field pattern of a scattered time harmonic wave by using a certain iterative regularization method. Aspects of all of the four fields of activities are involved in solving such an inverse problems.