GPU_PBTE: an efficient solver for three and four phonon scattering rates on graphics processing units.

Lattice thermal conductivity (LTC) is a key parameter for many technological applications. Based on the Peierls-Boltzmann transport equation (PBTE), many unique phonon transport properties of various materials were revealed. Accurate calculation of LTC with PBTE, however, is a time-consuming task, especially for compounds with a complex crystal structure or taking high-order phonon scattering into consideration. Graphical processing units (GPUs) have been extensively used to accelerate scientific simulations, making it possible to use a single desktop workstation for calculations that used to require supercomputers. Due to its fundamental differences from traditional processors, GPUs are especially suited for executing a large group of similar tasks with minimal communication, but require completely different algorithm design. In this paper, we provide a new algorithm optimized for GPUs, where a two-kernel method is used to avoid divergent branching. A new open-source code, GPU_PBTE, is developed based on the proposed algorithm. As demonstrations, we investigate the thermal transport properties of silicon and silicon carbide, and find that accurate and reliable LTC can be obtained by our software. GPU_PBTE performed on NVIDIA Tesla V100 can extensively improve double precision performance, making it two to three orders of magnitude faster than our CPU version performed on Intel Xeon CPU Gold 6248 @2.5 GHz. Our work also provides an idea of accelerating calculations with other novel hardware that may come out in the future.