A Novel Implementation of 2D3V Particle-in-Cell (PIC) Algorithm for Kepler GPU Architecture

The implementation of 2D-3v (2D in space and 3D in velocity space) PIC-MCC (Particle-In-Cell Monte Carlo Collision) method described in this paper involves the computational solution of Vlasov-Poisson equations, which provides the spatial and temporal evolution of the charged-particle velocity distribution functions in plasmas under the effect of self-consistent electromagnetic (EM) fields and collisions. Stringent numerical constraints associated with a PIC code makes it computationally prohibitive on CPUs in case of large problem sizes (total number of particles, number of grid points and simulation time-scale). We present the design and implementation of a Graphics Processing Unit (GPU) based 2D-3v PIC code using the CUDA C APIs for Kepler architecture. Several parallelization and optimization techniques have been presented in this paper with special emphasis on shuffle intrinsic specific to Nvidia Kepler architecture (or later), which significantly improves the performance compared to existing GPU implementations in the literature. On a test bed comprising of a serial implementation on Xeon E5 CPU and parallel implementations on Nvidia Tesla K40 graphics card, we have achieved a speedup of up to 60x in double precision mode. Effect of important numerical parameters on speedup has been investigated. Finally, we compare the performance of our best parallel implementation on different GPUs (Kepler as well as Maxwell) and analyze the effect of hardware architecture on the performance of the PIC code.