Bergische Universität Wuppertal Fachbereich Mathematik und Naturwissenschaften Angewandte Mathematik - Numerische Analysis (AMNA)

People Research Publications Teaching

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The lecture is suitable for students of mathematics as well as for physics.
The students of techno- or economathematics can use it as component AKap.NAaA-a "Selected Topics in Numerical Analysis and Algorithms" in the module of the same name.

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.