Ringvorlesung Wavephenomena (Winter Semester 2024/25)
- Lecturer: Prof. Dr. Roland Schnaubelt, Prof. Dr. Roland Griesmaier
- Classes: Lecture (0110500)
- Weekly hours: 2
Convolution Quadrature in Acoustic Obstacle Scattering
Dr. Marvin Knöller
In this course we study theoretical and practical aspects of acoustic wave propagation in presence of an impenetrable scattering object. The content of the lectures is twofold. In the first part we study the scattering problem for the wave equation and briefly recall existence and uniqueness of solutions by proceeding through the Laplace domain. Afterwards, we derive the all-at-once convolution quadrature approach for a semi-discretization in time. The second part is about the implementation of this method in Python using the boundary element library Bempp (see Bempp). This is planned as a live coding lecture, i.e., the code is developed in real time. Participants of this course are encouraged to bring their own laptops and actively engage in hands-on programming during the event.
The lectures take place on November 04, November 11, and November 18.
Normal Form and Space-Time Resonances for Wave-Type Equations
Dr. Louis Garenaux
In this part of the lecture, we will discuss two useful methods when studying the long-time behavior of PDE solutions. The normal form transform and the space-time integrations rely on a description of linear mode interactions through nonlinear terms. Thanks to a relatively simple algorithm, they allow to identify the irrelevant terms and to remove them from the equation. We will first set the stage, and present the impact of dimension and power exponents on the asymptotic behavior of solutions. Then, we will successively present both methods in various contexts and illustrate them on examples.
The lectures take place on November 25, December 02, and December 09.
Materials and Wave Phenomena in Optics: From Natural Media to Engineered Structures
Prof. Dr. Carsten Rockstuhl
In this part of the lecture series, we will explore the crucial role of materials in observing and controlling wave phenomena in optics and their mathematical description. Initially, we focus on natural materials, examining how their intrinsic optical properties can be integrated into Maxwell's equations. We discuss material-specific optical phenomena and their mathematical foundations. Then, we address artificial materials with subwavelength structures, demonstrating how these engineered materials can be treated as homogenous while exhibiting properties not found in nature. Finally, we investigate artificially periodically structured materials on length scales comparable to the wavelength of light. Considering these artificial materials enables new opportunities to manipulate light at the nanoscale, offering insights into novel applications in photonics.
The lectures take place on Dezember 16, January 16, and January 20.
Space and Time Discretization of Nonlinear Wave Equations
Dr. Benjamin Dörich
In this part of the lecture, we study nonlinear wave equations and their discretization in space and time. For completeness, we will introduce the main concepts of the spatial discretization by finite elements methods as well as basic tools from the numerical analysis of ordinary differential equations. First, we briefly recall the wellposedness theory of specific nonlinear wave equations using both semigroup and energy techniques. In a second step, we transfer these (two) approaches to the spatial discretization and show how rigorous error bounds can be obtained. We finally consider the fully discrete case where we combine both the spatial and temporal discretization to establish error bounds also for this case.
The lectures take place on January 27, February 03, and February 17.
| Schedule | ||
|---|---|---|
| Lecture: | Monday 14:00-15:30 | 20.30 1. OG R. 1.66/ 1.67 |