Parallelization of Particle-in-Cell Codes for Nonlinear Kinetic Models from Mathematical Physics

This paper considers the parallelization of two Particle-in-Cell (PIC) codes which simulate the time evolution of galaxies and globular clusters in the Newtonian or the general relativistic framework. The corresponding models are known as the Vlasov-Poisson or the Einstein-Vlasov system, and the latter is designed in particular to study the formation of black holes and space time singularities. We start with a step-by-step shared-memory parallelization of the Vlasov-Poisson code using POSIX Threads and finally develop message passing codes using MPI. The parallel codes have been investigated on three modern supercomputer systems using up to 4096 cores, and speedups above 1300 have been reached. The speedup obtained through parallelization has already helped in finding new numerical results, such as oscillating solutions of the Vlasov-Poisson system.