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Applied Mathematics and Mechanics (English Edition) ›› 2013, Vol. 34 ›› Issue (10): 1225-1236.doi: https://doi.org/10.1007/s10483-013-1740-x

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

李根1 唐春安2 李连崇2   

  1. 1. Department of Applied Mechanics and Engineering, School of Engineering, Sun Yat-sen University, Guangzhou 510275, P. R. China;
    2. Institute for Rock Instability and Seismicity Research, School of Civil Engineering, Dalian University of Technology, Dalian 116024, Liaoning Province, P. R. China
  • 收稿日期:2012-03-21 修回日期:2013-03-27 出版日期:2013-09-29 发布日期:2013-09-29

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

 LI Gen1, TANG Chun-An2, LI Lian-Chong2   

  1. 1. Department of Applied Mechanics and Engineering, School of Engineering, Sun Yat-sen University, Guangzhou 510275, P. R. China;
    2. Institute for Rock Instability and Seismicity Research, School of Civil Engineering, Dalian University of Technology, Dalian 116024, Liaoning Province, P. R. China
  • Received:2012-03-21 Revised:2013-03-27 Online:2013-09-29 Published:2013-09-29

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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 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-efficiency operations. By comparing with the numerical results, it is shown that the proposed method has the best performance.

关键词: improved preconditioned conjugate gradient (PCG) method, conjugate gradient method, large-scale linear equation, finite element method

Abstract: 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 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-efficiency operations. By comparing with the numerical results, it is shown that the proposed method has the best performance.

Key words: double homoclinic orbits, orbit flip, periodic orbit, resonance, improved preconditioned conjugate gradient (PCG) method, conjugate gradient method, large-scale linear equation, finite element method

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