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

Zhi-hui Zhu, Yang Feng, Xiao Yang, Hao Li, You Zou

Journal of Central South University ›› 2024, Vol. 31 ›› Issue (1) : 302-316. DOI: 10.1007/s11771-023-5474-6

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

Author information +
History +

Abstract

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.

Keywords

Seed-PCG method / linear equations with multiple right-hand sides / random vibration / GPU parallel computing / train-track-soil coupled model

Cite this article

Download citation ▾
Zhi-hui Zhu, Yang Feng, Xiao Yang, Hao Li, You Zou. An efficient parallel computing method for random vibration analysis of a three-dimensional train-track-soil coupled model using Seed-PCG algorithm. Journal of Central South University, 2024, 31(1): 302‒316 https://doi.org/10.1007/s11771-023-5474-6

References

[[1]]
Hu J, Bian X. Experimental and numerical studies on dynamic responses of tunnel and soils due to train traffic loads [J]. Tunnelling and Underground Space Technology, 2022, 128: 104628,
CrossRef Google scholar
[[2]]
Farahani M V, Sadeghi J, Jahromi S G, et al.. Modal based method to predict subway train-induced vibration in buildings [J]. Structures, 2023, 47: 557-572,
CrossRef Google scholar
[[3]]
Cao Z, Xu Y, Yuan Z, et al.. Nonstationary vibration responses of a three-dimensional tunnel-soil system excited by moving stochastic loads [J]. Computers and Geotechnics, 2020, 125: 103658,
CrossRef Google scholar
[[4]]
Yu H, Wang B, Li Y, et al.. A two-step framework for stochastic dynamic analysis of uncertain vehicle-bridge system subjected to random track irregularity [J]. Computers & Structures, 2021, 253: 106583,
CrossRef Google scholar
[[5]]
Wu B, Zeng Y, Zhou Z, et al.. Vibration prediction based on the coupling method of half-train model and 3D refined finite element ground model [J]. Computers and Geotechnics, 2021, 134: 104133,
CrossRef Google scholar
[[6]]
Wang L, Zhu Z, Costa P A, et al.. A framework combining pseudo-excitation method and two-and-a-half-dimensional finite element method for random ground vibrations induced by high-speed trains [J]. Advances in Structural Engineering, 2020, 23(15): 3263-3277,
CrossRef Google scholar
[[7]]
Wang L, Zhu Z, Bai Y, et al.. A fast random method for three-dimensional analysis of train-track-soil dynamic interaction [J]. Soil Dynamics and Earthquake Engineering, 2018, 115: 252-262,
CrossRef Google scholar
[[8]]
Jomo J N, De Prenter F, Elhaddad M, et al.. Robust and parallel scalable iterative solutions for large-scale finite cell analyses [J]. Finite Elements in Analysis and Design, 2019, 163: 14-30,
CrossRef Google scholar
[[9]]
Zhu Z, Xia Y, Wang L, et al.. A parallel computing method for three-dimensional random vibration of train-track-soil dynamic interaction based on GPU [J]. Journal of Hunan University(Natural Sciences), 2021, 48(7): 79-88 (in Chinese)
[[10]]
Jelich C, Karimi M, Kessissoglou N, et al.. Efficient solution of block Toeplitz systems with multiple right-hand sides arising from a periodic boundary element formulation [J]. Engineering Analysis with Boundary Elements, 2021, 130: 135-144,
CrossRef Google scholar
[[11]]
Amini S, Toutounian F, Gachpazan M. The block CMRH method for solving nonsymmetric linear systems with multiple right-hand sides [J]. Journal of Computational and Applied Mathematics, 2018, 337: 166-174,
CrossRef Google scholar
[[12]]
Heyouni M, Essai A. Matrix Krylov subspace methods for linear systems with multiple right-hand sides [J]. Numerical Algorithms, 2005, 40: 137-156,
CrossRef Google scholar
[[13]]
Chan T F, Wan W L. Analysis of projection methods for solving linear systems with multiple right-hand sides [J]. SIAM Journal on Scientific Computing, 1997, 18(6): 1698-1721,
CrossRef Google scholar
[[14]]
Gu G D. A seed method for solving nonsymmetric linear systems with multiple right-hand sides [J]. International Journal of Computer Mathematics, 2002, 79(3): 307-326,
CrossRef Google scholar
[[15]]
Mojarrab M, Toutounian F. Global LSMR (Gl-LSMR) method for solving general linear systems with several right-hand sides [J]. Journal of Computational and Applied Mathematics, 2017, 321: 78-89,
CrossRef Google scholar
[[16]]
Smith C F, Peterson A F, Mittra R. A conjugate gradient algorithm for the treatment of multiple incident electromagnetic fields [J]. IEEE Transactions on Antennas and Propagation, 1989, 37(11): 1490-1493,
CrossRef Google scholar
[[17]]
Sun D L, Huang T Z, Jing Y F, et al.. A block GMRES method with deflated restarting for solving linear systems with multiple shifts and multiple right-hand sides [J]. Numerical Linear Algebra with Applications, 2018, 25(5): e2148,
CrossRef Google scholar
[[18]]
Elbouyahyaoui L, Heyouni M. On applying weighted seed techniques to GMRES algorithm for solving multiple linear systems [J]. Boletim da Sociedade Paranaense de Matemática, 2018, 36(3): 155-172,
CrossRef Google scholar
[[19]]
Abdel-Rehim A M, Morgan R B, Wilcox W. Improved seed methods for symmetric positive definite linear equations with multiple right-hand sides [J]. Numerical Linear Algebra with Applications, 2014, 21(3): 453-471,
CrossRef Google scholar
[[20]]
Kalantzis V, Bekas C, Curioni A, et al.. Accelerating data uncertainty quantification by solving linear systems with multiple right-hand sides [J]. Numerical Algorithms, 2013, 62: 637-653,
CrossRef Google scholar
[[21]]
LI X, LIU H, ZHU J. MINRES seed projection methods for solving symmetric linear systems with multiple right-hand sides [J]. Mathematical Problems in Engineering, 2014, 2014. DOI: https://doi.org/10.1155/2014/357874.
[[22]]
Li C, Xiong B, Qiang J, et al.. Multiple linear system techniques for 3D finite element method modeling of direct current resistivity [J]. Journal of Central South University, 2012, 19(2): 424-432,
CrossRef Google scholar
[[23]]
ABDEL-REHIM A, MORGAN R B, WILCOX W. Seed methods for linear equations in lattice qcd problems with multiple right-hand sides [J]. PoS-Proceedings of Science, 2009, lattice 2008. DOI: https://doi.org/10.48550/arXiv.0901.3512.
[[24]]
Chen X, Wang D, Ren J, et al.. Application of hybrid CPU-GPU computing platform in large-scale geotechnical finite element analysis [J]. China Civil Engineering Journal, 2016, 49(6): 105-112 (in Chinese)
[[25]]
Liu J, Xian Z, Zhou Y, et al.. A marker-and-cell method for large-scale flow-based topology optimization on GPU [J]. Structural and Multidisciplinary Optimization, 2022, 65(4): 125,
CrossRef Google scholar
[[26]]
Lopes P C F, Pereira A M B, Clua E W G, et al.. A GPU implementation of the PCG method for large-scale image-based finite element analysis in heterogeneous periodic media [J]. Computer Methods in Applied Mechanics and Engineering, 2022, 399: 115276,
CrossRef Google scholar
[[27]]
Liu J, Du Y, Du X, et al.. 3D viscous-spring artificial boundary in time domain [J]. Earthquake Engineering and Engineering Vibration, 2006, 5(1): 93-102,
CrossRef Google scholar
[[28]]
Zhu Z, Wang L, Gong W, et al.. Study on vertical random vibration of train-bridge coupled system based on improved iteration model [J]. Journal of Hunan University (Natural Sciences), 2016, 43(11): 120-130 (in Chinese)
[[29]]
Lu F, Lin J H, Kennedy D, et al.. An algorithm to study non-stationary random vibrations of vehicle-bridge systems [J]. Computers & Structures, 2009, 87(3–4): 177-185,
CrossRef Google scholar
[[30]]
Fan W, Sheng X, Li Z, et al.. The higher-order analysis method of statistics analysis for response of linear structure under stationary non-Gaussian excitation [J]. Mechanical Systems and Signal Processing, 2022, 166: 108430,
CrossRef Google scholar
[[31]]
He X, Shi K, Wu T. An efficient analysis framework for high-speed train-bridge coupled vibration under non-stationary winds [J]. Structure and Infrastructure Engineering, 2020, 16(9): 1326-1346,
CrossRef Google scholar

Accesses

Citations

Detail

Sections
Recommended

/