应用改进算法的对称逐步超松弛预处理共轭梯度法进行大体积混凝土仿真计算

Application of symmetric successive over relaxation-preconditioned conjugate gradient method with improved algorithm in numerical simulation of massive concrete

针对大体积混凝土有限元仿真计算中存在计算规模大、计算时间长的问题,为克服使用直接解法导致占用内存多、耗时长和精度得不到保证的缺点,充分考虑大体积混凝土结构有限元仿真分析中温度场和位移场求解的特点,用改进算法的对称逐步超松弛预处理共轭梯度法取代直接解法,进行温度场和位移场计算中大型稀疏对称正定线性方程组的求解.采用算例计算对比了使用2种方法计算的内存占用、耗时和计算精度等情况,结果表明,该方法可完全消除整体劲度矩阵带宽对存储空间需求的影响,减少内存占用和计算耗时,且使得计算精度可灵活控制.

With regard to problems of large scale computation and excessive run time in the numerical simulation of massive concrete using the FEM,and in order to overcome the disadvantages of high memory occupancy rate,excessive run time,and low accuracy using straightforward methods,the symmetric successive over relaxation-preconditioned conjugate gradient method with an improved algorithm can be employed to replace the straightforward methods with full consideration of the characteristics of solving temperature and displacement fields of massive concrete structures with finite element simulations. The large-sized sparse symmetric positive definite linear equations for the temperature and displacement fields were solved. The memory occupancies,run time,and accuracies of the two methods were compared through computation examples. The results show that the proposed method can completely eliminate the influence of the bandwidth of the integral stiffness matrix on the storage space requirement,reduce the physical memory occupancy and run time,and flexibly controlling the accuracy.