A linear wave hitting a diffraction grating

Описание: This is a variant of the recent video    • Classics revisited: A diffraction grating   of a diffraction grating, but with a linear wave instead of a circular wave. The linear wave hits the grating at a small angle, since this creates more interesting interference patterns that when hitting it head on. Note that while the wave height representation shows waves moving to the right, they have an envelope that is mostly stationary. The second part of the video makes this envelope more visible.
Diffraction gratings are optical devices that can have weird effects on light, such as splitting it into several beams traveling in different directions. This simulation illustrates such an effect for waves encountering a grating made of evenly spaced circular obstacles.
The video has two parts, showing the same simulation with two different color schemes:
Wave height: 0:00
Average energy (log scale): 1:29
In the first part, the color hue shows the wave height. In the second part, it shows the energy, averaged from the beginning of the simulation, on a logarithmic scale. There are oscillating boundary conditions on the left border of the simulation, and absorbing boundary conditions on the right one. Since periodic boundary conditions between the top and bottom would not go well with the waves arriving at an angle, the simulation uses a solution of the 1D wave equation there.

Render time: 23 minutes 1 second
Color scheme: Part 1 - Twilight by Bastian Bechtold
https://github.com/bastibe/twilight
Part 2 - Inferno by Nathaniel J. Smith and Stefan van der Walt
https://github.com/BIDS/colormap

Music: "Open Sea Morning" by Puddle Of Infinity

See also https://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 https://hplgit.github.io/fdm-book/doc...
C code: https://github.com/nilsberglund-orlea...
https://www.idpoisson.fr/berglund/sof...
Many thanks to Marco Mancini and Julian Kauth for helping me to accelerate my code!

#wave_equation #waves #diffraction #diffraction_grating