Abstract：A multilevel hierarchical parallel modal synthesis algorithm (MHPMSA) for large-scale finite element modal analysis was proposed based on the sparse storage techniques and parallel conventional modal synthesis algorithm (PCMSA). Based on two-level partitioning and quartic transformation strategies, the proposed method not only improves memory access rate through the distributed sparse storage of a large amount of data, but also reduces the solution time of the interface equation through the reduction in interface equations’ size. Moreover, a multilevel hierarchical parallelization of the computational procedure is introduced to enable the separation of the communication of inter-nodes, heterogeneous-core-groups and inside- heterogeneous-core-groups through mapping computing tasks to various hardware layers, which can not only efficiently achieve the load balancing at different layers, but also significantly improve communication rate through the hierarchical communication. Hence, it can improve the efficiency rates of parallel computing of large-scale finite element modal analysis by fully exploiting the architecture characteristics of heterogeneous multicore clusters. Test results show that, compared with the PCMSA, the proposed method with sparse storage format can considerably save memory space and significantly improve computational efficiency.
[1] 范宣华,肖世富,陈璞.千万自由度量级有限元模态分析并行计算研究[J].振动与冲击,2015,34(17):77-82.
FAN Xuanhua, XIAO Shifu, CHEN Pu. Parallel computing for finite element modal analysis with over ten-million-DOF [J]. Journal of Vibration and Shock, 2015, 34(17)：77-82.
[2] Kennedy GJ, Martins JRRA. A parallel finite-element frameworks for large-scale gradient-based design optimization of high-performance structures [J]. Finite Elements in Analysis and Design, 2014, 87:56-73.
[3] P.H. Ni, S.S. Law. Hybrid computational strategy for structural damage detection with short‐term monitoring data [J]. Mechanical Systems and Signal Processing, 2016, 70-71:650–663.
[4] Wang YY, Gu Y, Liu JL. A domain-decompotition generalized finite difference method for stress analysis in three-dimensional composite materials [J]. Applied Mathematics letters, 2020, 104: 106226.
[5] M. Łoś, R. Schaefer, M. Paszyński. Parallel space–time hp adaptive discretization scheme for parabolic problems [J]. Journal of Computational and Applied Mathematics, 2018, 344:819-355.
[6] Xinqiang Miao, Xianlong Jin, Junhong Ding. Improving the parallel efficiency of large-scale structural dynamic analysis using a hierarchical approach [J]. International Journal of High Performance Computing Applications, 2016, 30(2):156-168.
[7] Bai Z, Demmel J, Dongarra J, et al. Templates for the solution of algebraic eigenvalue problems: A practical guide [M]. SIAM, Philadelphia, 2000.
[8] Watkins D S. The matrix eigenvalue problem: GR and krylov subspace mtehods [M]. SIAM, Philadelphia, 2007.
[9] S.Sundar, B. K. Bhagavan. Generalized eigenvalue problems: Lanczos algorithm with a recursive partitioning method [J]. Computers & Mathematics with Applications, 2000, 39(7):211-224.
[10] Congying Duan, Zhongxiao Jia. A global harmonic Arnoldi method for large non-Hermitian eigenproblems with an application to multiple eigenvalue problems [J]. Journal of computational and Applied Mathematics, 2010, 234(3): 845-860.
[11] Stewart G W. A Krylov-Schur algorithm for large eigenproblems[J]. SIAM Journal on Matrix Analysis & Applications, 2001, 23(3):601-614.
[12] Michael Rippl, Bruno Lang, Thomas Huckle. Parallel eigenvalue computation for banded generalized eigenvalue problems[J]. Parallel Computing, 2019, 88:102542.
[13] Bao Rong, Kun Lu, Xiaojun Ni, Jian Ge. Hybrid finite element transfer matrix method and its parallel solution for fast calculation of large-scale structural eigenproblem [J]. Applied mathematical modeling, 2020, 11:169-181.
[14] B.C.P.Heng, R.I.Macke. Parallel modal analysis with concurrent distributed objects [J]. Computers and structures, 2010, 88:1444-1458.
[15] Yuji Aoyama, Genki Yagawa. Compoment mode synthesis for large-scale structural eigenanalysis. Computers and structures, 2001,79:605-615.
[16] Petr Paˇrík, Jin-Gyun Kim, Martin Isoz, Chang-uk Ahn. A parallel approach of the enhanced craig-bampton method [J]. Mathematics, 2021, 9:3278.
[17] Leonardo Gasparini, José R.P. Rodrigues, Douglas A. Augusto, Luiz M. Carvalho, et al. Hybrid parallel iterative sparse linear solver framework for reservoir geomechanical and flow simulation [J]. Journal of Computational Science, 2021, 51:101330.
[18] Pieter Ghysels, Ryan Synk. High performance sparse multifrontal solvers on modern GPUs [J]. Parallel Computing, 2022, 110:102897.
[19] Jie Cui, Gangtie Zheng. An iterative state-space component modal synthesis approach for damped systems [J]. Mehchanical systems and signal processing, 2020, 142:106558.
[20] Chang-uk Ahn, Soo Min Kim, Dong Il Park, Jin-Gyun Kim. Refining characteristic constraint modes of component mode synthesis with residual modal flexibility [J]. Mechanical systems and signal processing, 2022, 178:1092
