Research on parallel computing of magnetic L-shell based on OpenMP

In the study of radiation belts, the (L, B) coordinate system reduces the three-dimensional problem to a two-dimensional problem, greatly improving the utilization of the limited three-dimensional observational data on radiation belts. The L-shell is one of the most important parameters in the (L, B) coordinate system. It is widely used in particle characteristics analysis, in the description of spacecrafts' orbital radiation environments, and in radiation band modeling. The L-shell is calculated as the integral of the magnetic line tracing, but the complexity of geomagnetic field configurations results in the strict limitation of the tracking step length, resulting in more steps consisting of a single tracking calculation. In addition, the tracking path and distance of different spatial position lines vary significantly with time and space. This variation results in the independence of many L-shell calculations from one another, with different levels of complexity. In such cases the summation of steps may not be able to be simplified, causing the calculation speed to be slow and the efficiency low. In order to improve the efficiency of the L-shell calculation, this paper uses OpenMP to realize singlemachine multithreading parallelization of L-shell calculation programs widely used at present. This paper then analyzes the acceleration ratio and efficiency boost of parallelization. The results show that the efficiency of L-shell calculation is much improved by parallel processing. When the number of threads is set equal to the maximum number of threads in the system (here, 8), parallel performance is optimal. The acceleration ratio ranges from 1.57 to 2.81, and the parallelization efficiency boost ranges from 19.63% to 35.13%. Load imbalance among threads is the main factor affecting parallel performance. In order to improve the parallel acceleration ratio and efficiency boost, this paper proposes a sort factor, representing the complexity of L-value calculation. Based on this, an algorithm of sorting and redistribution (sort, S) is proposed for load optimization. The effects of four methods of optimizing load imbalance are compared and analyzed: dynamic, sort+"S", sort+dynamic, and sort+"S"+dynamic. The results show that the sort + dynamic method provides the best optimization, increasing the optimization efficiency by 6.12%-9.50%. Using this method, the acceleration ratio ranges from 2.33 to 3.30, and the efficiency boost ranges from 29.13% to 41.25%. This paper shows that OpenMP can successfully parallelize and improve the computing efficiency of L-values. As for the problem of load imbalance, the best parallel acceleration ratio and efficiency boost can be achieved using sort+dynamic adjustment. This investigation provides a useful exploration of efficiency improvement for spatial physics and other fields that leverage similar types of big data analysis research. © 2021, Science Press. All right reserved.