Numerical methods for wave-type equations

M. Wess, TU Wien, Institute of Analysis and Scientific Computing, SS 2024

This jupyter-book serves as lecture notes for the lecture Numerical methods for wave-type equations held by Markus Wess at the TU Wien, Institute of Analysis and Scientific Computing in SS2024.

It covers the theoretical, as well as the practical part of the lecture. As this is the first time this lecture is held, the notes will be updated and enhanced regularly to progress with the lecture.

The practical part uses the open source library Netgen/NGSolve, basics will be covered throughout the lecture.

Table of Contents

• 1. Mathematical modeling of wave phenomena
• 2. Basic numerical methods for time-domain waves
• 3. Basic numerical methods for frequency domain wave problems
• 4. Time-integration
• 5. Explicit methods for time-domain waves
• 6. Perfectly Matched Layers
• 7. Eigenvalue Problems

References

[CK19]

David Colton and Rainer Kress. Inverse acoustic and electromagnetic scattering theory. Volume 93 of Applied Mathematical Sciences. Springer, Cham, fourth edition, 2019.

[DorflerW23]

Willy Dörfler and Christian Wieners. Space-time approximations for linear acoustic, elastic, and electro- magnetic wave equations. In Wave Phenomena: Mathematical Analysis and Numerical Approximation, volume 49 of Oberwolfach Seminars. Birkhäuser Cham, 2023.