Numerical Evaluation of Stable and OpenMP Parallel Face-Based Smoothed Point Interpolation Method for Geomechanical Problems

Compared with the finite element method (FEM), the meshfree smoothed point interpolation method (SPIM) has a more accurate stiffness and is not sensitive to mesh distortion, which has high potential in solving engineering problems. In this study, an effective simulation program based on the face-based SPIM was developed and was applied to solve geomechanical problems. To enhance the reliability of the SPIM program when dealing with large-scale and nonlinear problems, the line search algorithm, the adaptive sub-step method, and the OpenMP parallel design were adopted to enhance the convergence, stability, and computational efficiency. The test results of the slope stability analysis show that the SPIM program is correct when compared with the Bishop method. Moreover, the SPIM program has an asymptotic quadratic convergence and satisfactory stability, even when the slope is in a critical state. In addition, for large-scale examples, the speedup ratio of the OpenMP parallel program can achieve a speedup ratio of 6~8 on a computing platform with 20 CPU cores, and the maximum speedup ratio for a single load step can reach 14.50. Finally, future work on the developing face-based SPIM simulation program is discussed.