Study on GPU Parallel Speedup and Application of FE-EFG Coupling Method

doi:10.3901/JME.2018.11.197

Abstract

Abstract: The finite element (FE)-element free Galerkin (EFG) coupling method can make full use of the respective advantages of finite element method and element-free Galerkin method. In order to further improve the computational efficiency of FE-EFG coupling method in large-scale engineering application, Graphic processing unit parallel speedup algorithm of coupled FE-EFG method is presented. Nodes or integral points in the nodal influence field, and the nodes in the integral point definition field are found efficiently by using the local search method in the EFG domain. Based on the characteristics of compute unified device architecture (CUDA), the idea of interacting node pair is introduced to parallel assemble the total stiffness matrix and store it by compress sparse row storage format. The preconditioned conjugate gradient is used to solve the total discrete equations based on the CUDA library function. Two numerical examples verified the feasibility and computational accuracy of presented coupling method. The results show that computational efficiency of FE-EFG coupling method is improved remarkably, and its speedup ratio will increase with the increase of computing scale. Thus, a highly efficient coupling algorithm is offered to large-scale engineering computation.

Key words: collocation approach, coupled FE-EFG method, GPU parallel computing, interaction node pair, local search method

CLC Number:

TH123
O241

GONG Shuguang, LIAO Yuli, XIE Guilan, ZHANG Jianping. Study on GPU Parallel Speedup and Application of FE-EFG Coupling Method[J]. Journal of Mechanical Engineering, 2018, 54(11): 197-204.

References

[1] BOKIN M E, BENNETT J A. Shape optimization of three-dimension folded plate structures[J]. AIAA Journal, 1985, 23(11):1804-1810.
[2] BELYTSCHKO T, LU Y Y, GU L. Element-free Galerkin methods[J]. International Journal for Numerical Methods in Engineering, 1994, 37(2):229-256.
[3] BELYTSCHKO T, ORGAN D, KRONGAUZ Y. A coupled finite element-element-free Galerkin method[J]. Computational Mechanics, 1995, 17(3):186-195.
[4] HUERTA A. Enrichment and coupling of the finite element and meshless methods[J]. International Journal for Numerical Methods in Engineering, 2000, 48(11):1615-1636.
[5] XIAO Q Z, DHANASEKAR M. Coupling of FE and EFG using Collocation Approach[J]. Advances in Engineering Software, 2002, 33(s7-10):507-515.
[6] 杨海天,刘岩.一种FEM-EFGM耦合技术及其应用[J].计算力学学报, 2003, 20(5):511-517. YANG Haitian, LIU Yan. A coupled FEM-EFGM technique and its application[J]. Chinese Journal of Computational Mechanics, 2003, 20(5):511-517.
[7] RAO B N, RAHMAN S. A coupled Mesh-Finite element method for fracture analysis of cracks[J]. International Journal of Pressure Vessels & Piping, 2001, 78(9):647-657.
[8] GONG Shuguang, XIE Guilan, ZHANG Jianping, et al. Sensitivity analysis and shape optimization based on FE-EFG coupled method[J]. Research in Engineering Design, 2008, 20(2):117-128.
[9] WANG Zhongjin, YUAN Binxian. Numerical analysis of coupled finite element with element-free Galerkin in sheet flexible-die forming[J]. Transactions of Nonferrous Metals Society of China, 2014, 24(2):462-469.
[10] MARTÍNEZ-FRUTOS J, HERRERO-PÉREZ D. Efficient matrix-free GPU implementation of fixed grid finite element analysis[J]. Finite Elements in Analysis & Design, 2015, 104(1):61-71.
[11] CAI Yong, LI Guangyao, WANG Hu. A parallel nodebased solution scheme for implicit finite element method using GPU[J]. Procedia Engineering, 2013, 61:318-324.
[12] 蔡勇,王琥,李光耀,等. 基于边光滑三角形壳元和统一计算架构的板料成形仿真并行计算方法[J]. 机械工程学报, 2012, 48(6):32-38. CAI Yong, WANG Hu, LI Guangyao, et al. Parallel simulation of sheet metal forming based on EST element and compute unified device architecture[J]. Journal of Mechanical Engineering, 2012, 48(6):32-38.
[13] 龚曙光,刘奇良,卢海山,等. 无网格Galerkin法GPU加速并行计算及其应用[J]. 计算力学学报,2015,32(6):745-751. GONG Shuguang, LIU Qiliang, LU Haishan, et al. Parallel computing and application of Element-Free Galerkin method for GPU acceleration[J]. Chinese Journal of Computational Mechanics, 2015, 32(6):745-751.
[14] 龚曙光,卢海山,张建平,等. 基于交叉节点对无网格Galerkin法的改进算法研究[J]. 工程力学, 2015, 32(8):16-21,28. GONG Shuguang, LU Haishan, ZHANG Jianping, et al. Study on an improved algorithm of element-free Galerkin method based on interacting nodal pairs[J]. Engineering Mechanics, 2015, 32(8):16-21,28.
[15] KARATARAKIS A, METSIS P, PAPADRAKAKIS M. GPU-acceleration of stiffness matrix calculation and efficient initialization of EFG meshless methods[J]. Computer Methods in Applied Mechanics & Engineering, 2013, 258(5):63-80.