朱志辉1,2?覮,夏禹涛1,王力东3,刘禹兵1.基于GPU的车辆-轨道-地基土耦合系统 3D随机振动并行计算方法[J].湖南大学学报:自然科学版,2021,(7):79~88
基于GPU的车辆-轨道-地基土耦合系统 3D随机振动并行计算方法
A Parallel Computing Method for Three-dimensional Random Vibration of Train-track-soil Dynamic Interaction Based on GPU
  
DOI:
中文关键词:  随机振动  GPU并行计算  3D有限元法  虚拟激励法  车辆-轨道-地基土耦合模型
英文关键词:random vibration  GPU parallel computing  three dimensional finite element method  pseudo-excitation method  train-track-soil couple model
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作者单位
朱志辉1,2?覮,夏禹涛1,王力东3,刘禹兵1 (1. 中南大学 土木工程学院湖南 长沙 410075 2. 中南大学 高速铁路建造技术国家工程实验室湖南 长沙410075 3. 长沙理工大学 土木工程学院湖南 长沙 410114) 
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中文摘要:
      针对轨道不平顺随机特征导致车辆-轨道-地基土耦合系统随机分析计算效率低的问题,采用虚拟激励法降低大样本分析的计算量;针对耦合系统等效刚度矩阵的稀疏特性,采用行压缩(Compressed Sparse Row,CSR)格式存储大型稀疏矩阵,采用预处理共轭梯度法(Preconditioned Conjugate Gradient,PCG)求解对称正定的等效静力平衡方程,最后通过MATLAB-CUDA(Compute Unified Device Architecture)混合平台开发基于GPU的并行计算程序. 数值算例表明:基于MATLAB-CUDA混合平台求解等效静力平衡方程的效率是串行多点同步算法的86.13倍,大大缩短了随机振动分析的总计算时间,且内存占用小、易于在个人计算机上实施;采用PCG法求解车辆-轨道-地基土耦合系统形成的大型稀疏线性方程组时,建议以加速度指标作为迭代收敛精度的控制指标;可通过选取适当的迭代收敛精度,以达到计算精度和计算效率的平衡.
英文摘要:
      Aiming at the issue of low efficiency in the random analysis and calculation of train-track-soil coupled system due to the random characteristics of track irregularity,the pseudo-excitation method(PEM) is used to reduce the computing cost of large samples. Considering the sparsity of equivalent stiffness matrix of train-track-soil coupling system,the large-scale sparse matrix was stored in Compressed Sparse Row(CSR) format. The symmetric positive definite equation of equivalent static equilibrium is solved by the preconditioned conjugate gradient(PCG) method,and the parallel program is developed by the MATLAB-CUDA(Compute Unified Device Architecture) hybrid platform. The numerical example shows that the efficiency of solving equivalent static equilibrium equation based on MATLAB-CUDA hybrid platform is 86.13 times that of the multi-point synchronization algorithm,which greatly reduces the total calculation time of the random vibration analysis,and the memory usage is small and it is easy to implement on a personal computer. When using PCG method to solve the large sparse linear equations of vehicle-track-foundation soil coupling system,it is suggested to take the acceleration as the control index of convergence accuracy of iteration. By choosing the appropriate convergence accuracy of iteration,the balance of calculation accuracy and efficiency is achieved.
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