Finite element parallel computing based on minimal residual-preconditioned conjugate gradient method

doi:10.11772/j.issn.1001-9081.2015.12.3387

Journal of Computer Applications ›› 2015, Vol. 35 ›› Issue (12): 3387-3391.DOI: 10.11772/j.issn.1001-9081.2015.12.3387

• Advanced computing • Previous Articles Next Articles

Finite element parallel computing based on minimal residual-preconditioned conjugate gradient method

FU Chaojiang^1,2, CHEN Hongjun¹

1. College of Civil Engineering, Fujian University of Technology, Fuzhou Fujian 350180, China;
2. Fujian Provincial Key Laboratory of Advanced Technology and Informatization in Civil Engineering, Fuzhou Fujian 350180, China

Received:2015-05-25 Revised:2015-07-16 Online:2015-12-10 Published:2015-12-10

基于残余平滑预处理共轭梯度算法的有限元并行计算

付朝江^1,2, 陈洪均¹

1. 福建工程学院土木工程学院, 福州 350108;
2. 福建省土木工程新技术与信息化重点实验室, 福州 350108

通讯作者: 付朝江(1966-),男,江西九江人,教授,博士,主要研究方向:并行计算、数值分析
作者简介:陈洪均(1986-),男,陕西榆林人,硕士研究生,主要研究方向:结构材料非线性有限元分析。
基金资助:
国家自然科学基金资助项目(51378124)。

Abstract

Abstract: Finite element analysis for elastic-plastic problem is very time-consuming. A parallel substructure Preconditioned Conjugate Gradient (PCG) algorithm combined with Minimal Residual (MR) smoothing was proposed under the environment of Message Passing Interface (MPI) cluster. The proposed method was based on domain decomposition, and substructure was treated as isolated finite element model via the interface conditions. Throughout the analysis, each processor stored only the information relevant to its substructure and generated the local stiffness matrix. A parallel substructure oriented preconditioned conjugate gradient method was developed, which combined with MR smoothing and diagonal storage scheme. Load balance was discussed and interprocessor communication was optimized in the parallel algorithm. A substepping scheme to integrate elastic-plastic stress-strain relations was used. The errors in the integration process were controlled by adjusting the substep size automatically according to a prescribed tolerance. Numerical example was implemented to validate the performance of the proposed PCG algorithm on workstation cluster. The performance of the proposed PCG algorithm was analyzed and the performance was compared with conventional PCG algorithm. The example results indicate that the proposed algorithm has good speedup and efficiency and is superior in performance to the conventional PCG algorithm. The proposed algorithm is efficient for parallel computing of 3D elastic-plastic problems.

Key words: Preconditioned Conjugate Gradient (PCG) algorithm, Message Passing Interface (MPI), parallel computing, domain decomposition, finite element

摘要： 针对弹塑性问题的有限元分析非常耗时,基于消息传递接口(MPI)集群环境,提出了残余平滑的子结构预处理共轭梯度并行算法。采取区域分解,将子结构通过界面条件处理为独立的有限元模型。整体分析时,每个处理器仅存储与其相关的子结构信息并生成局部刚度矩阵。采用对角存储方式和最小残余平滑法,设计出了结合残余平滑(MR)的并行子结构预处理共轭梯度(PCG)算法。并行算法中对负载平衡进行了探讨,对处理器间的通信进行了优化。利用子步法对弹塑性应力应变进行积分,根据预定的容许值自动调整每个子步的大小来控制积分过程的误差。在工作站集群上实现了数值算例,分析了算法的性能,计算性能与传统的PCG算法进行了比较。算例显示:所提算法具有良好的加速比和效率,优于传统的PCG算法,对弹塑性问题的有限元分析,是一种有效的并行求解算法。

关键词: 预处理共轭梯度法, 消息传递接口, 并行计算, 区域分解, 有限元

CLC Number:

TP301.6
TP31

FU Chaojiang, CHEN Hongjun. Finite element parallel computing based on minimal residual-preconditioned conjugate gradient method[J]. Journal of Computer Applications, 2015, 35(12): 3387-3391.

付朝江, 陈洪均. 基于残余平滑预处理共轭梯度算法的有限元并行计算[J]. 计算机应用, 2015, 35(12): 3387-3391.

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Finite element parallel computing based on minimal residual-preconditioned conjugate gradient method

基于残余平滑预处理共轭梯度算法的有限元并行计算

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