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基于异构计算平台的混合撕裂有限元求解优化技术

张鋆宸1, 张纪林1, 冯仰德2, 王珏2, 聂宁明2, 丁佳明3   

  1. 1. 杭州电子科技大学计算机学院, 杭州电子科技大学网络空间安全学院, 复杂系统建模与仿真教育部重点实验室, 杭州 310018;
    2. 中国科学院计算机网络信息中心, 北京 100190;
    3. 杭州电子科技大学计算机学院, 杭州 310018
  • 收稿日期:2021-02-24 发布日期:2022-06-10
  • 通讯作者: 冯仰德,Email:ydfeng@sccas.cn.
  • 基金资助:
    国家重点研发计划(2017YFB0202302)和浙江省重点研发计划项目(2019C01059)

张鋆宸, 张纪林, 冯仰德, 王珏, 聂宁明, 丁佳明. 基于异构计算平台的混合撕裂有限元求解优化技术[J]. 数值计算与计算机应用, 2022, 43(2): 202-220.

Zhang Yunchen, Zhang Jilin, Feng Yangde, Wang Jue, Nie Ningming, Ding Jiaming. OPTIMIZATION TECHNIQUES FOR HTFETI METHOD ON HETEROGENEOUS COMPUTING PLATFORM[J]. Journal on Numerica Methods and Computer Applications, 2022, 43(2): 202-220.

OPTIMIZATION TECHNIQUES FOR HTFETI METHOD ON HETEROGENEOUS COMPUTING PLATFORM

Zhang Yunchen1, Zhang Jilin1, Feng Yangde2, Wang Jue2, Nie Ningming2, Ding Jiaming3   

  1. 1. College of Computer Science, Hangzhou Dianzi University, Hangzhou 310018, China;School of Cyberspace, Hangzhou Dianzi University, Hangzhou 310018, China;Key laboratory of Complex Systems Modeling and Simulation Ministry of Education, Hangzhou 310018, China;
    2. Computer Network Information Center, Beijing 100190, China;
    3. College of Computer Science, Hangzhou Dianzi University, Hangzhou 310018, China
  • Received:2021-02-24 Published:2022-06-10
混合撕裂有限元法(Hybrid Total Finite Element Tearing and Interconnecting method,HTFETI)适用于求解结构力学、热力学等问题,是一种非重叠的区域分解方法,适用于大规模求解.但是在异构计算平台上对反应堆堆芯组件进行数值模拟时,采用混合撕裂有限元法会出现进程内和进程间的负载不均衡现象.在混合撕裂有限元求解器中,最主要的计算是稠密矩阵向量乘.针对进程内和进程间出现的负载不均衡现象,本文实现了动态负载均衡技术,充分利用了节点内和节点间的处理器资源,加快求解速度.最后,本文通过数值实验验证了上述优化技术能够加快混合撕裂有限元法的求解速度8.2\%$\sim$9.4\%.
The Hybrid Total Finite Element Tearing and Interconnecting (HTFETI) method is suitable for solving structural mechanics, thermodynamics and other problems. It is a nonoverlapping domain decomposition method and is suitable for large-scale solutions. However, when the reactor core assembly is numerically simulated on the heterogeneous computing platform, the HTFETI method will lead to load imbalance within and between processes. The most important calculation is dense matrix vector multiplication in the HTFETI solver. In view of the load imbalance within and between processes, this paper implements the dynamic load balancing technology, which makes full use of the processor resources within and between nodes to speed up the solution speed. Finally, numerical experiments show that the above optimization technique can accelerate the solving speed of HTFETI method 8.2%~9.4%.

MR(2010)主题分类: 

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[1] Farhat C, Roux F X. A method of finite element tearing and interconnecting and its parallel solution algorithm[J]. International journal for numerical methods in engineering, 1991, 32(6):1205-1227.
[2] Dostál Z, Horák D, Kučera R. Total FETI-an easier implementable variant of the FETI method for numerical solution of elliptic PDE[J]. Communications in Numerical Methods in Engineering, 2006, 22(12):1155-1162.
[3] Markopoulos A, R′ıha L, Brzobohat′y T, Kučera R, Meca O, Kozubek T. Treatment of singular matrices in the Hybrid total FETI method[G]. In Domain Decomposition Methods in Science and Engineering XXIII, Springer, 2017, 237-244.
[4] Sojka R, Horák D, Hapla V, Cermák M. The impact of enabling multiple subdomains per MPI process in the TFETI domain decomposition method[J]. Applied Mathematics and Computation, 2018, 319:586-597.
[5] Dostál Z, Vlach O, Brzobohat′y T. Scalable TFETI based algorithm with adaptive augmentation for contact problems with variationally consistent discretization of contact conditions[J]. Finite Elements in Analysis and Design, 2019, 156:34-43.
[6] Dostál Z, Horák D, Brzobohat`y T, Vodstrčil P. Bounds on the spectra of Schur complements of large H-TFETI-DP clusters for 2D Laplacian[J]. Numerical Linear Algebra with Applications, 2020, e2344.
[7] Roux F X, Farhat C. Parallel implementation of direct solution strategies for the coarse grid solvers in 2-level FETI method[J]. Contemporary Mathematics, 1998, 218:158-173.
[8] Jarošsová M, Kozubek T, Menšs′ık M, Markopoulos A. Hybrid total FETI method. ECCOMAS 2012[C]. In European Congress on Computational Methods in Applied Sciences and Engineering, e-Book Full Papers, Vienna University of Technology, 2012, 6653-6663.
[9] Klawonn A, Rheinbach O. Highly scalable parallel domain decomposition methods with an application to biomechanics[J]. ZAMM-Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik:Applied Mathematics and Mechanics, 2010, 90(1):5-32.
[10] Klawonn A, Radtke P, Rheinbach O. FETI-DP methods with an adaptive coarse space[J]. SIAM Journal on Numerical Analysis, 2015, 53(1):297-320.
[11] Klawonn A, Lanser M, Rheinbach O, Uran M. Nonlinear FETI-DP and BDDC methods:a unified framework and parallel results[J]. SIAM Journal on Scientific Computing, 2017, 39(6):C417-C451.
[12] Toivanen J, Avery P, Farhat C. A multilevel FETI-DP method and its performance for problems with billions of degrees of freedom[J]. International Journal for Numerical Methods in Engineering, 2018, 116(10-11):661-682.
[13] Klawonn A, Kühn M J, Rheinbach O. Parallel adaptive FETI-DP using lightweight asynchronous dynamic load balancing[J]. International Journal for Numerical Methods in Engineering, 2020, 121(4):621-643.
[14] R′ıha L, Brzobohat`y T, Markopoulos A, Kozubek T, Meca O, Schenk O, Vanroose W. Efficient implementation of total feti solver for graphic processing units using schur complement[C]. In International Conference on High Performance Computing in Science and Engineering, Springer, 2015, 85-100.
[15] Vavr′ık R, R′ıha L. Acceleration Techniques for FETI Solvers for GPU Accelerators[C]. In 2018 International Conference on High Performance Computing&Simulation (HPCS), IEEE, 2018, 546-553.
[16] 满足大规模运算需求AMD发表ROCm开源平台[J].今日电子, 2016,(12):\nobreakspace 46.
[17] Babej M, Jääskeläinen P. HIPCL:Tool for Porting CUDA Applications to Advanced OpenCL Platforms Through HIP[C]. In Proceedings of the International Workshop on OpenCL, 2020, 1-3.
[18] 陈建龙,张小向.矩阵分解与广义逆矩阵[J].大学数学, 2020, 36(05):\nobreakspace 57-66.
[19] R′ıha L, Brzobohat′y T, Markopoulos A, Meca O, Kozubek T. Massively Parallel Hybrid Total FETI (HTFETI) Solver[C]. In Proceedings of the Platform for Advanced Scientific Computing Conference, PASC'16, New York, NY, USA, 2016. Association for Computing Machinery.
[20] Toselli A, Widlund O. Domain decomposition methods-algorithms and theory[M]. Springer Science&Business Media, 2006, 34.
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