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.
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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)
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Li, G., Tang, Ca. & Li, Lc. High-efficiency improved symmetric successive over-relaxation preconditioned conjugate gradient method for solving large-scale finite element linear equations. Appl. Math. Mech.-Engl. Ed. 34, 1225–1236 (2013). https://doi.org/10.1007/s10483-013-1740-x
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DOI: https://doi.org/10.1007/s10483-013-1740-x
Key words
- improved preconditioned conjugate gradient (PCG) method
- conjugate gradient method
- large-scale linear equation
- finite element method