Bergische Universität Wuppertal Fachbereich Mathematik und Naturwissenschaften Applied and Computational Mathematics (ACM)

Team Research Publications Teaching

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This is a course on the mathematical modeling of wave phenomena in application areas such as acoustics, geophysics, radio waves, and optics. We consider mathematical methods for solving various types of PDEs related to wave propagation in concrete practical situations. The goal of the course is also to provide students with a large toolbox of mathematical techniques that can be used when dealing with various real-world problems of applied mathematics. Furthermore, by approaching the modeling of wave propagation in different ways, we will try to highlight certain connections between different areas of mathematics and physics.

Topics of the Lecture:

1. Wave equation and Helmholtz equation, guided waves, solution by Fourier method
2. parabolic equations theory for sound and radio waves
3. normal modes and mode-based solution techniques
4. iterative parabolic equations
5. invariant imbedding method
6. practical applications in underwater acoustics: shallow- and deep-water waveguides, shallow-to-deep scenario
7. noise monitoring and mitigation, impact onto marine fauna
8. effective propagation velocities and acoustic ranging
9. whispering-gallery waves in a shallow sea
10. Practical classes: implementing a simple solver of Helmholtz equation (normal modes), a parabolic equation solver, noise impact assessment tool.

Literature:

Previous knowledge: Analysis I - III, basic knowledge of ordinary differential equations.

Exercises: Exercise Sheets, Materials

Criteria: Regular participation and participation in the exercise groups, as well as reaching 50% of the possible points on the first seven or the remaining exercise sheets and at least 2/3 of the possible points for the practical tasks.