This is a 3D rendering of the simulation [ Ссылка ] showing a circular phased array emitting four beams, in which the observer turns around the array.
Phased arrays are computer-controlled antennas, whose phase is altered in such a way that the emitted signal propagates only in certain directions, without moving the antennas. Antennas sending multiple beams are used in wireless communication to send several signals at once. If the antenna is well-designed, one can assign a different signal to each beam.
The array shown here consists of 25 sources, that emit signals with a phase shift of 1/15th of a period. The following parameters have been changed compared to symmetrical set-ups as shown in the video [ Ссылка ] :
- The radius of the circle of emitters has been reduced, so that it is comparable to half the wavelength.
- The amplitude of the emitters depends on their position: it is proportional to 1 + cos(2*Pi*n/25).
- The frequency is the same for all emitters, but has been increased compared to the previous simulation. What probably matters most is the wavelength resulting from the chosen wave speed and frequency, and how it relates to the distance between sources.
The video has two parts, showing the same simulation with two different color schemes:
Wave height: 0:00
Averaged energy: 1:31
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. There are absorbing boundary conditions on the outer boundaries of the simulation. Here the direction-dependence of the beams is more visible in the energy representation. In the wave height representation, it appears as slight phase shifts between the wave fronts along certain directions.

Render time: 1 hour 5 minutes
Color scheme: Part 1 - Cividis by Jamie R. Nuñez, Christopher R. Anderton, Ryan S. Renslow
[ Ссылка ]
Part 2 - Inferno by Nathaniel J. Smith and Stefan van der Walt
[ Ссылка ]

Music: "Boom Bap Flick" by Quincas Moreira@QuincasMoreira

See also [ Ссылка ] 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 [ Ссылка ]
C code: [ Ссылка ]
[ Ссылка ]
Many thanks to Marco Mancini and Julian Kauth for helping me to accelerate my code!

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