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Ringvorlesung Wave Phenomena (Summer Semester 2020)

Due to the corona crisis the iRTG lecture series has been postponed to the coming winter semester 2020/21.

In the iRTG lecture series four members of CRC 1173 will talk about topics whithin the analysis and numerics of wave phenomena. The lectures are directed to Ph.D. students (in particular of the integrated research training group of CRC 1173) and to advanced master students with a solid background in partial differential equations. The series is organized by Roland Griesmaier and Roland Schnaubelt.

Lecture: Monday 14:00-15:30 SR 1.067

An alternative starting point for electromagnetism

Dr. Ivan Fernandez Corbaton

The aim of these lectures is to provide a simple introduction to an unconventional approach to electromagnetism. From the start, the prominent role of the electric and magnetic fields is taken over by two other fields. These fields represent the two handedness that Maxwell solutions can have. The use of this alternative set of fields has notable advantages over the electric and magnetic fields: Decoupled evolution equations, relativistic invariance, and the remarkable ability to split the two possible handedness in electromagnetism.

The lectures take place on April 20, April 27, and May 4.

Dr. Ivan Fernandez Corbaton, is postoctoral researcher at the Insitute of Nanotechnology at KIT.

High-frequency nonlinear optics

Prof. Dr. Tobias Jahnke

We consider a class of semilinear hyperbolic systems which includes the Maxwell-Lorentz equations in a dispersive medium as one special case. Both the evolution equation and the initial data involve a factor 1/\epsilon with a small parameter \epsilon. As a consequence, typical solutions oscillate with frequency O(1/\epsilon) in time and space and have to be computed on time intervals of length O(1/\epsilon) to observe physically interesting effects. Approximating such solutions numerically is a very challenging task.

In the three lectures, we will focus on the analytical instead of the numerical approximation. Following the classical approach, we derive a nonlinear Schrödinger equation with a non-oscillatory solution which allows to approximate the solution of the original problem up to an error of O(\epsilon). This will be discussed in detail. Finally, an approach for the construction of numerical methods for high-frequency nonlinear optics will be sketched.

The lectures take place on Mai 11, Mai 18, and Mai 25.

Wave front sets and propagation of singularities

Prof. Dr. Peer Kunstmann

The lectures take place on June 8, June 15, and June 22.

Inverse source problems

Prof. Dr. Roland Griesmaier

In this lecture series we discuss theoretical aspects and numerical reconstruction algorithms for the inverse source problem for acoustic and electromagnetic waves. This is a classical inverse problem which is well-known to be underdetermined and notoriously instable.

After briefly introducing the basic concepts of time-harmonic wave propagation and recalling some traditional regularization schemes for the inverse source problem, we will focus on more recent developments. We consider the convex source support, which is a novel solution concept for the inverse source problem. Then we discuss the inverse problems of wave splitting and data completion and show how these can be utilized in the inverse source problem. Finally we present uncertainty principles for acoustic and electromagnetic waves that can be used to establish stability estimates for the aforementioned inverse problems.

The lectures take place on June 29, July 6, and July 13.