基于Seed-PCG法的列车-轨道-地基土三维随机振动GPU并行计算方法  

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

作　　者：朱志辉 冯杨 杨啸 李昊 邹有 ZHU Zhi-hui;FENG Yang;YANG Xiao;LI Hao;ZOU You(National Engineering Research Center of High-speed Railway Construction Technology,Changsha 410075,China;School of Civil Engineering,Central South University,Changsha 410075,China;School of Computer Science and Engineering,Center South University,Changsha 410083,China;Information and Network Center,Central South University,Changsha 410083,China)

机构地区：[1]National Engineering Research Center of High-speed Railway Construction Technology,Changsha 410075,China [2]School of Civil Engineering,Central South University,Changsha 410075,China [3]School of Computer Science and Engineering,Center South University,Changsha 410083,China [4]Information and Network Center,Central South University,Changsha 410083,China

出　　处：《Journal of Central South University》2024年第1期302-316,共15页中南大学学报（英文版）

基　　金：Project(2022YFB2603301) supported by the National Key R&D Program of China。

摘　　要：为了解决列车-轨道-地基土三维有限元模型随机多样本计算效率低的问题,本文提出了一种基于Seed-PCG法的高效并行计算方法。基于有限元法和虚拟激励法建立轨道不平顺激励下的三维列车-轨道-地基土耦合随机振动分析模型;针对车致地基土随机振动分析产生的多右端项线性方程组求解问题,采用Seed-PCG方法进行求解。通过PCG方法求解种子系统得到的Krylov子空间进行投影,以改进其余线性方程组的初始解和对应的初始残量,有效提高了PCG法的收敛速度,最后,在MATLABCUDA混合平台上开发了并行计算程序。数值算例表明:相同计算平台下的该方法相比多点同步算法获得了104.2倍的加速;相比PCG法逐个求解方案减少了18%的迭代次数,获得了1.21倍的加速。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 threedimensional(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.

关 键 词：Seed-PCG法 多右端项线性方程组 随机振动 GPU并行计算 列车-轨道-地基土耦合模型 

分 类 号：TP332[自动化与计算机技术—计算机系统结构] U211.3[自动化与计算机技术—计算机科学与技术]