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High-efciency improved symmetric successive over-relaxation preconditioned conjugate gradient method for solving large-scale finite element linear equations

ISSN号：0253-4827
期刊名称：《应用数学和力学：英文版》
时间：0
分类：TP311.1[自动化与计算机技术—计算机软件与理论;自动化与计算机技术—计算机科学与技术] TP311.52[自动化与计算机技术—计算机软件与理论;自动化与计算机技术—计算机科学与技术]
作者机构：[1]Sun Yat Sen Univ, Sch Engn, Dept Appl Mech & Engn, Guangzhou 510275, Guangdong, Peoples R China, [2]Dalian Univ Technol, Sch Civil Engn, Inst Rock Instabil & Seism Res, Dalian 116024, Liaoning Provin, Peoples R China
相关基金：Project supported by the National Natural Science Foundation of China （Nos. 51309261, 41030747, 41102181, and 51121005）, the National Basic Research Program of China （973 Program）（No. 2011CB013503）, and the Young Teachers＇ Initial Funding Scheme of Sun Yat-sen University （No. 39000-1188140）

作者：李根, 唐春安, 李连崇

关键词：预处理共轭梯度法, 大型线性方程组, 有限元分析, 松弛, 对称, 计算机辅助制造, 计算机辅助工程, 求解, improved preconditioned conjugate gradient （PCG） method, conjugate gradient method, large-scale linear equation, finite element method

中文摘要：

Fast solving large-scale linear equations in the finite element analysis is a classical subject in computational mechanics. It is a key technique in computer aided engineering(CAE) and computer aided manufacturing(CAM). This paper presents a high-efciency improved symmetric successive over-relaxation(ISSOR) preconditioned conjugate gradient(PCG) method, which maintains the convergence and inherent parallelism consistent with the original form. Ideally, the computation can be reduced nearly by 50% as compared with the original algorithm. It is suitable for high-performance computing with its inherent basic high-efciency operations. By comparing with the numerical results, it is shown that the proposed method has the best performance.

英文摘要：

Fast solving large-scale linear equations in the finite element analysis is a classical subject in computational mechanics. It is a key technique in computer aided engineering （CAE） and computer aided manufacturing （CAM）. This paper presents a high-efficiency improved symmetric successive over-relaxation （ISSOR） preconditioned conjugate gradient （PCG） method, which maintains lelism consistent with the original form. Ideally, the by 50% as compared with the original algorithm. the convergence and inherent paralcomputation can It is suitable for be reduced nearly high-performance computing with its inherent basic high-efficiency operations. By comparing with the numerical results, it is shown that the proposed method has the best performance.