Efficiency Analysis of Spherical Harmonic Synthesis Based on MPI Parallel Algorithm

The spherical harmonic synthesis formula for calculating the parameters of the earth gravity field was analyzed. In order to avoid repeated calculation of the recursive coefficients of cos(mλ), sin (mλ) and Legendre functions in the traditional algorithm, this paper proposes the method of pre-storage array reference, and then combined with MPI (message passing interface) parallel technology to further improve computational efficiency. The experiment adopted the 2 160 degree EGM2008 model to calculate the grid gravity anomaly at resolutions 1° and 5' on the DELL PowerEdge R730 server and Tianhe-2 supercomputer respectively. Experimental results show that the way of array reference reduces the computing workload of CPU (central processing unit), but at the same time increases the memory access times, suitable for the computing platform with relatively ordinary CPU performance and high memory frequency. MPI parallel technology can give full play to the advantage of multi-core computer, greatly improve the computational efficiency of spherical harmonic synthesis, and obtain the maximum speedup ratio when the number of processes is equal to the number of logical CPUs.