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

Guangye Chen, Luis Chacon, Daniel C. Barnes
Oak Ridge National Laboratory, Oak Ridge,TN 37831, USA
arXiv:1111.5295v1 [physics.plasm-ph] (22 Nov 2011)


   author={Chen}, G. and {Chac{‘o}n}, L. and {Barnes}, D.~C.},

   title={"{An efficient mixed-precision, hybrid CPU-GPU implementation of a fully implicit particle-in-cell algorithm}"},

   journal={ArXiv e-prints},




   keywords={Physics – Plasma Physics, Physics – Computational Physics},




   adsnote={Provided by the SAO/NASA Astrophysics Data System}


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Recently, a fully implicit, energy- and charge-conserving particle-in-cell method 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-free Newton-Krylov (JFNK) solver, capable of using very large timesteps without loss of numerical stability or accuracy. A fundamental feature of the method is the segregation of particle-orbit computations from the field solver, while remaining fully self-consistent. This paper describes a very efficient, mixed-precision hybrid CPU-GPU implementation of the implicit PIC algorithm exploiting this feature. The JFNK solver is kept on the CPU in double precision (DP), while the implicit, charge-conserving, and adaptive particle mover is implemented on a GPU (graphics processing unit) using CUDA in single-precision (SP). Performance-oriented optimizations are introduced with the aid of the roofline model. The implicit particle mover algorithm is shown to achieve up to 400 GOp/s on a Nvidia GeForce GTX580. This corresponds to 25% absolute GPU efficiency against the peak theoretical performance, and is about 300 times faster than an equivalent serial CPU (Intel Xeon X5460) execution. For the test case chosen, the mixed-precision hybrid CPU-GPU solver is shown to over-perform the DP CPU-only serial version by a factor of sim 100, without apparent loss of robustness or accuracy in a challenging long-timescale ion acoustic wave simulation.
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