This simulation was suggested by several viewers, following the simpler version • How a parabolic antenn... . It shows the evolution of a circular wave, emitted from the focus of a parabolic antenna. The part of the wave reflected on the antenna is transformed into a planar wave, which travels to the facing parabola with almost no loss of energy. The second parabola transforms the wave back into part of a circular wave, which is then concentrated in its focal point. In this way, signals can be transmitted over much longer distances than shown in this simulation, with little loss of power. Note that non-planar waves are also concentrated near a point, which is however different from the parabolas' focal point.
The colors indicate the energy of the wave: blue means low energy, red means high energy. The boundary conditions in the simulation are absorbing, but do not work perfectly, which is why you see some reflections from the sides of the outer rectangle.
Edit: For a new version with a different color scheme, see • Speak to me: Waves tra...
Music: "The Rising" by Aakash Gandhi@discobiscuit1320
See also images.math.cnrs.fr/Des-ondes... for more explanations (in French) on a few previous simulations of wave equations.
The simulation solves the wave equation by discretization. The algorithm is adapted from the paper hplgit.github.io/fdm-book/doc...
C code: github.com/nilsberglund-orlea...
www.idpoisson.fr/berglund/sof...
Many thanks to my colleague Marco Mancini for helping me to accelerate my code!
26 авг 2021
