Accelerating Non-equilibrium Ionization Calculation Through GPU-based Computing

The efficient calculation of the radiation mechanism has been a hot topic in astrophysical simulation,and non-equilibrium ionization(NEI)is one of the difficulties.Currently,some excellent tools had been developed for astrophysical simulation,of which only FLASH and ENZO support solving the NEI,yet only for a few elements.The rest only provide the expansion interface of NEI computation.Randall Simth et al from CFA have done a lot of work on NEI.They provide the Libapecnei library dedicated to various NEI calculations.Libapecnei is a CPU-based solver that is limited by the performance bottlenecks of the CPU.The GPU has a distinct advantage over the CPU in terms of computing power and memory bandwidth.Therefore,GPU can be used to accelerate NEI calculation and to gain significant performance benefits.NEI calculation is computation-intensive and data-interdependent,and its core task is to solve ordinary differential equations(ODE).Focused on the above characteristics,a series of GPU-based NEI calculation method is presented in this paper.Firstly,a GPU-optimized fourth-order Runge-Kutta algorithm was designed to solve ODE in NEI.Meanwhile,the calculation of NEI was broken into two parts: equation establishing and equation solving.We designed two solutions named majoroptimization and full-optimization base on different migrate contents.The majoroptimization migrated the equation solving part to the GPU,and the full-optimization migrated two parts.Then,we compared the performance of different optimizations.Secondly,we improved the GPU-based NEI calculation performance by GPU memory multiplexing,GPU memory alignment,merging memory accesses,reasonable data division and thread division.Finally,in order to evaluate the computational performance in different frameworks,we designed NEI calculation method with MPI in multi-core CPU and multi-core CPU-GPU architecture.Experiments showed that the acceleration result using the complete migration method is more efficient than the whole NEI calculation.The speedup can reach 212.7 times by optimizing the NEI calculation method of GPU.Moreover our multi-core CPU-GPU-based NEI calculation scheme can make full use of the GPU NEI calculation performance.