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