Particle In Cell code in Julia

This software is developed in order to experiment optimizations and to try the best way to have an efficient package for particle-mesh numerical methods for plasmas.

It is a work in progress, you can find first tests in the documentation.

I compared performances of this Julia code with a Fortran version that solves same equation with same parameters and same numerical method. You can find it here. This is an old code written in 2005 with Régine Barthelmé and even is is not well optimized, it takes only 6 seconds with 204800 particles. I note here times of this Julia code and what I have done to speed-up things.

• 323 seconds : First version
• 303 seconds : Use julia -O3 --check-bounds=no
• 302 seconds : change shape of positions and velocities arrays for particles
• 156 seconds : Regroup ex, ey, and bz in a same array eb(3,nx,ny)
• 176 seconds : put the array ebj in fdtd type
• 140 seconds : put the particles data in one array, the particle push_v is now very fast.
• 077 seconds : replace the julia interpolation function by a call to the fortran subroutine.
• 019 seconds : replace the julia deposition by a call to the fortran subroutine
• 006 seconds : vectorize and use views in function push_x instead of a loop
• 135 seconds : back to julia functions for particles but without mod1 calls.
• 003 seconds : back to julia functions, I set the types of struct members. I let some of them with the type Any, very bad idea...

Now I increase the number of particles to 1024000 and begin to parallelize particles motion.

• 58 seconds : First serial time, It spends 24 seconds in push_x, we can do better.
• 46 seconds : Move interpolation step inside the push_v function and reduce memory print.
• 31 seconds : Add @threads in push_x and push_v functions. My CPU has 4 cores.
• 17 seconds : by adding @threads in compute_current

• ParticleInCell.jl by Luke Adams.
• MPIParticleInCell.jl by Luke Adams.
• ElectrostaticPIC1D.jl by James Cook.
• Julia discourse thread

The simulations in the following papers have been made with this code. Some of them are implemented in FORTRAN translated in Julia. Both codes are in the repository. The interface and code are messy, sorry for that. Don't hésitate to contact me or use the Discussions tab.

• P. Chartier, N. Crouseilles, M. Lemou, F. Méhats, X. Zhao, Uniformly accurate methods for three dimensional Vlasov equations under strong magnetic field with varying direction, SIAM J. Sc. Comput. 42, pp. 520-547, 2020.
• P. Chartier, N. Crouseilles, M. Lemou, F. Méhats, X. Zhao, Uniformly accurate methods for Vlasov equations with non-homogeneous strong magnetic field, Math. Comp. 88, pp. 2697-2736, 2019.
• P. Chartier, N. Crouseilles, X. Zhao, Numerical methods for the two-dimensional Vlasov-Poisson models in the finite Larmor radius approximation regime, J. Comput. Phys., 375, pp. 619-640, 2018.
• N. Crouseilles, S. Hirstoaga, X. Zhao, Multiscale Particle-in-Cell methods and comparisons for the long time two-dimensional Vlasov-Poisson equation with strong magnetic field, Comput. Phys. Comm. 222, pp. 136-151, 2018.
• N. Crouseilles, M. Lemou, F. Méhats, X. Zhao, Uniformly accurate Particle-In-Cell method for the long time solution of the two-dimensional Vlasov-Poisson equation with uniform strong magnetic field, J. Comput. Phys. 346, pp. 172-190, 2017.
• N. Crouseilles, M. Lemou, F. Méhats, X. Zhao, Uniformly accurate forward semi-Lagrangian methods for highly oscillatory Vlasov-Poisson equations, SIAM MMS 15, pp. 723-744, 2017.