An efficient parallel computing method for random vibration analysis of a three-dimensional train-track-soil coupled model using Seed-PCG algorithm

This study proposes an efficient parallel computation method based on Seed-preconditioned Conjugate Gradient (Seed-PCG) algorithm, to address the issue of computational inefficiency of random multi-sample in three-dimensional (3D) finite element (FE) model of train-track-soil. A 3D train-track-soil coupled random vibration analysis model is established using the finite element method (FEM) and the pseudo-excitation method (PEM) under track irregularity excitation. The Seed-PCG method is utilized to solve the system of linear equations with multiple right-hand sides arising from the random analysis of the vehicle-induced ground vibration. Furthermore, by projecting the Krylov subspace obtained from solving the seed system by the PCG method, the initial solution of the remaining linear equation systems and the corresponding initial residuals are improved, leading to an effective enhancement of the convergence speed of the PCG method. Finally, the parallel computing program is developed on a hybrid MATLAB-Compute Unified Device Architecture (CUDA) platform. Numerical examples demonstrate the effectiveness of the proposed method. It achieves 104.2 times acceleration compared with the multi-point synchronization algorithm (MPSA) proposed by author ZHU under the same computing platform. Moreover, compared with the PCG method, the number of iterations is reduced by 18 % and the acceleration is increased by 1.21 times.