High Performance Computation and DEM Software Development

The high-performance parallel computing approaches mainly include the open multi-processing method (OpenMP) (Amritkar et al. in J Comput Phys 256:501–519, 2014), the message passing interface (MPI) (Kačianauskas et al. in Adv Eng Softw 41:52–63, 2010), and the MPI-OpenMP algorithm (Berger et al. in Powder Technol 278:234–247, 2015). The above three methods use the CPU as the computing core, and the cores cooperate with each other to improve the calculation efficiency (Kačeniauskas et al. in Adv Eng Softw 42:237–246, 2011). In addition, the parallel algorithms based on a graphics processing unit (GPU) have been successfully used for large-scale computations in the discrete element method (Zhang et al. in Adv Eng Softw 60–61:70–80, 2013). Compared to a CPU, the number of computing cores in a GPU is significantly increased, and the hardware costs of the computer are reduced, which makes the GPU have more powerful parallel computing capabilities (Xu et al. in Particuology 9:446–450, 2011). The GPU parallel computing method for spheres was applied to simulate large-scale granular systems with a wide range of sizes (He et al. in Powder Technol 333:219–228, 2018). Another GPU parallel algorithm for the multi-sphere model was used to analyze the effects of the process parameters on large-scale tablet coating processes (Boehling et al. in Eur J Pharm Sci off J Eur Feder Pharm Sci 90:14–24, 2016). Moreover, considering the computational requirements of non-spherical DEM simulations, the ellipsoidal GPU parallel approach was developed and used to compare the speedup ratio of a GPU to a CPU (Gan et al. in Powder Technol 301:1172–1182, 2016). The polyhedral GPU parallel method was validated and successfully applied to the hopper discharge (Govender et al. in J Comput Appl Math 270:386–400, 2014, in Appl Math Comput 319:318–336, 2018). The coating process of 20 million biconvex tablets in a rotating drum was simulated by a GPU parallel algorithm (Kureck et al. in Chem Eng Sci 202:462–480, 2019). However, thus far, few efforts have been made to contribute to the detailed description of GPU parallel algorithms for superquadric elements.