Implementation and Optimization of a 1D2V PIC Method for Nonlinear Kinetic Models on GPUs

This paper considers the parallel numerical simulation of the time evolution of galaxies and globular clusters on GPUs. The model used is the Einstein-Vlasov system, which is designed, in particular, to study the formation of black holes and spacetime singularities in a general relativistic framework.First, a reference implementation is derived using NVIDIA CUDA as programming model, which is then optimized in several steps. Bottlenecks are identified by profiling, and different approaches, namely particle sort, improved treatment of atomic operations, and kernel fusion are investigated to overcome these bottlenecks. Each optimized variant is evaluated in relation to the other variants using detailed runtime experiments and profiling results. Using in the order of 10
⁷
to 10
⁸
particles, speedups between 1.84 and 2.38 w.r.t. the reference implementation have been observed.