GPU-accelerated smoothed particle finite element method for large deformation analysis in geomechanics

Particle finite element method (PFEM) is an effective numerical tool for solving large-deformation problems in geomechanics. By incorporating the node integration technique with strain smoothing into the PFEM, we proposed the smoothed particle finite element method (SPFEM). This paper extends the SPFEM to three-dimensional cases and presents a SPFEM executed on graphics processing units (GPUs) to boost the computational efficiency. The detailed parallel computing strategy on GPU is introduced. New computation formulations related to the strain smoothing technique are proposed to save memory space in the GPU parallel computing. Several benchmark problems are solved to validate the proposed approach and to evaluate the GPU acceleration performance. Numerical examples show that with the new formulations not only the memory space can be saved but also the computational efficiency is improved. The computational cost is reduced by similar to 70% for the double precision GPU parallel computing with the new formulations. Compared with the sequential CPU simulation, the GPU-accelerated simulation results in a significant speedup. The overall speedup ranges from 8.21 to 11.17 for double-precision simulations. Furthermore, the capability of the GPU-accelerated SPFEM in solving large-scale complicated problems is demonstrated by modelling the progressive failure of a long slope with strain softening soil.