Abstract 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 ~ 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.

中文翻译：

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用于地质力学大变形分析的 GPU 加速平滑粒子有限元方法

摘要 粒子有限元法(PFEM)是求解地质力学大变形问题的有效数值工具。通过将具有应变平滑的节点集成技术纳入 PFEM，我们提出了平滑粒子有限元方法 (SPFEM)。本文将 SPFEM 扩展到三维情况，并提出了在图形处理单元 (GPU) 上执行的 SPFEM 以提高计算效率。详细介绍了GPU上的并行计算策略。提出了与应变平滑技术相关的新计算公式，以节省 GPU 并行计算中的内存空间。解决了几个基准问题以验证所提出的方法并评估 GPU 加速性能。数值算例表明，新公式不仅可以节省内存空间，而且可以提高计算效率。使用新公式的双精度 GPU 并行计算的计算成本降低了约 70%。与顺序 CPU 仿真相比，GPU 加速的仿真带来了显着的加速。双精度模拟的整体加速范围从 8.21 到 11.17。此外，GPU 加速的 SPFEM 在解决大规模复杂问题方面的能力通过对具有应变软化土壤的长边坡的渐进破坏进行建模来证明。与顺序 CPU 仿真相比，GPU 加速的仿真带来了显着的加速。双精度模拟的整体加速范围从 8.21 到 11.17。此外，GPU 加速的 SPFEM 在解决大规模复杂问题方面的能力通过对具有应变软化土壤的长边坡的渐进破坏进行建模来证明。与顺序 CPU 仿真相比，GPU 加速的仿真带来了显着的加速。双精度模拟的整体加速范围从 8.21 到 11.17。此外，GPU 加速的 SPFEM 在解决大规模复杂问题方面的能力通过对具有应变软化土壤的长边坡的渐进破坏进行建模来证明。