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Recently, a fully implicit, energy- and charge-conserving particle-in-cellmethod has been proposed for multi-scale, full-f kinetic simulations [G. Chen,et al., J. Comput. Phys. 230,18 (2011)]. The method employs a Jacobian-freeNewton-Krylov (JFNK) solver, capable of using very large timesteps without lossof numerical stability or accuracy. A fundamental feature of the method is thesegregation of particle-orbit computations from the field solver, whileremaining fully self-consistent. This paper describes a very efficient,mixed-precision hybrid CPU-GPU implementation of the implicit PIC algorithmexploiting this feature. The JFNK solver is kept on the CPU in double precision(DP), while the implicit, charge-conserving, and adaptive particle mover isimplemented on a GPU (graphics processing unit) using CUDA in single-precision(SP). Performance-oriented optimizations are introduced with the aid of theroofline model. The implicit particle mover algorithm is shown to achieve up to400 GOp/s on a Nvidia GeForce GTX580. This corresponds to 25% absolute GPUefficiency against the peak theoretical performance, and is about 300 timesfaster than an equivalent serial CPU (Intel Xeon X5460) execution. For the testcase chosen, the mixed-precision hybrid CPU-GPU solver is shown to over-performthe DP CPU-only serial version by a factor of \sim 100, without apparent lossof robustness or accuracy in a challenging long-timescale ion acoustic wavesimulation.

An efficient mixed-precision, hybrid CPU-GPU implementation of a fully implicit particle-in-cell algorithm