The task of wave scattering is to analyze the effect an object has on a wave when both collide. Scattering problems arise in various different applications, for example in computer tomography, radar or historically in Rutherfords discovery of atomic nuclei.
Mathematically, the problem can be described using partial differential equations. In the so called direct scattering problem, given an incident wave u^i, and an object D, we are interested in computing the scattered wave u^s.
Provided the incident wave is a time acoustic plane wave, the total field u = u^i+u^s can be described by the so called Helmholtz equation.
A second interesting case is given by using time-harmonic electromagnetic plane-waves as incident waves, which leads to studying the Maxwell equations.
In applications like radar, not the scattered field is of interest, but rather the shape of the object, which caused the scattering effect. This leads to so called inverse problems, where
knowledge of the scattered field u^s is used to reconstruct the object D.
Solving the inverse scattering problem is considerably more difficult than solving the direct problem, as it involves nonlinear and ill-posed problems. An aim of this seminar is to present techniques, like regularization methods, to deal with these difficulties.
