The optimization with half-precision floating-point numbers for 3-D seismic simulation based on the curved grid finite-difference method

Large-scale and high-resolution earthquake simulations are very significant to earthquake hazard evaluation and exploration seismology. However, high-resolution earthquake simulations require large computing and storage resources, which increase the economic cost of computing. Compared with single-precision floating-point numbers (FP32), half-precision floating-point numbers (FP16) have faster calculation speed and lower storage requirements, which have been applied to computing platforms such as Nvidia GPUs, Sunway series supercomputers, and Ascend processors. However, the stored range of FP16 is very narrow, and numerical overflow or underflow may occur during the calculations. Therefore, in order to solve the wave equations stably, we introduce two scaling factors Cv and Cs, and rescale physical quantities to the range of the stored values of FP16. Thus, we derive new equations, which can be calculated with FP16. Based on half-precision floating-point arithmetic operations, we develop a multi-GPU earthquake simulation solver using the curved grid finite-difference method (CGFDM). Moreover, we perform several simulations and compare the seismograms with the standard CGFDM to verify the solver. Consequently, the calculation efficiency is remarkably improved, and the memory usage is reduced to 1/2.