Tool to create videos of particles or waves in different 2D domains.

Created by Nils Berglund and optimized by Marco Mancini

C code for videos on YouTube Channel https://www.youtube.com/c/NilsBerglund

Parameter values used in specific simulations will be gradually added to file Parameters.md, Parameters_June21.md and so on.

There are two groups of 5 files and 10 files:

Simulations of classical particles in billiards.

1. global_particles.c: global variables and parameters
2. sub_part_billiard.c: drawing/computation routines common to particle_billiard and drop_billiard
3. particle_billiard.c: simulation of a collection of non-interacting particles in a billiard
4. drop_billiard.c: simulation of an expanding front of particles
5. particle_pinball.c: variant of particle_billiard with some extra statistics plots

• Create subfolders tif_part, tif_drop
• Customize constants at beginning of .c file
• Compile with

gcc -o particle_billiard particle_billiard.c-O3 -L/usr/X11R6/lib -ltiff -lm -lGL -lGLU -lX11 -lXmu -lglut

gcc -o drop_billiard drop_billiard.c-O3 -L/usr/X11R6/lib -ltiff -lm -lGL -lGLU -lX11 -lXmu -lglut

• Many laptops claim to have 4 cores, but two of those are virtual. OMP acceleration may be more effective after executing

export OMP_NUM_THREADS=2

in the shell before running the program

• Generate movie with

ffmpeg -i part.%05d.tif -vcodec libx264 part.mp4

Simulations of wave equation, heat equation and Schrodinger equation.

1. global_pdes.c: global variables and parameters
2. sub_wave.c: drawing/computation routines common to wave_billiard, heat and schrodinger
3. sub_wave_comp.c: some modified functions needed by wave_comparison
4. common_wave.c: common functions of wave_billiard and wave_comparison
5. wave_billiard.c: simulation of the (linear) wave equation
6. wave_comparison.c: comparison of the wave equation in two different domains
7. wave_energy.c: a version of wave_billiard plotting the energy profile of the wave
8. mangrove.c: a version of wave_billiard with additional features to animate mangroves
9. heat.c: simulation of the heat equation, with optional drawing of gradient field lines
10. schrodinger.c: simulation of the Schrodinger equation

• Create subfolders tif_wave, tif_heat, tif_schrod
• Customize constants at beginning of .c file
• Compile with

gcc -o wave_billiard wave_billiard.c -L/usr/X11R6/lib -ltiff -lm -lGL -lGLU -lX11 -lXmu -lglut -O3 -fopenmp

gcc -o wave_comparison wave_comparison.c -L/usr/X11R6/lib -ltiff -lm -lGL -lGLU -lX11 -lXmu -lglut -O3 -fopenmp

gcc -o heat heat.c -L/usr/X11R6/lib -ltiff -lm -lGL -lGLU -lX11 -lXmu -lglut -O3 -fopenmp

gcc -o schrodinger schrodinger.c -L/usr/X11R6/lib -ltiff -lm -lGL -lGLU -lX11 -lXmu -lglut -O3 -fopenmp

• Many laptops claim to have 4 cores, but two of those are virtual. OMP acceleration may be more effective after executing

export OMP_NUM_THREADS=2

in the shell before running the program

• Generate movie with

ffmpeg -i wave.%05d.tif -vcodec libx264 wave.mp4

Some references

• Discretizing the wave equation: https://hplgit.github.io/fdm-book/doc/pub/wave/pdf/wave-4print.pdf
• Absorbing boundary conditions: https://hal.archives-ouvertes.fr/hal-01374183
• Cloaking device: https://www.sciencedirect.com/science/article/pii/S0165212514001759
• Poisson disc sampling: https://bl.ocks.org/mbostock/dbb02448b0f93e4c82c3