关键词: 岩土工程, 非连续变形分析, 子矩阵技术, 刚度矩阵存储, 线性方程组求解, 块雅可比迭代与预处理的块共轭梯度法

Abstract: Simulating large-scale engineering problems with discontinuous deformation analysis (DDA) is extremely time-consuming. The solving process of linear equations normally costs more than 70% of the total computing time, and thus the computing efficiency of algorithms for linear equations is a significant research topic. Firstly, two contents of non-zero storage in the DDA have been described. One is the block compressed sparse row method, and the other is the iterative scheme of non-zero position recording based on the trial-error approach. Secondly, in view of the sub-matrix technology, the block Jacobi (BJ) iteration method and pre-processing block conjugate gradient (PCG, including Jacobi and symmetric successive over relaxation(SSOR)pre-processing) iteration method have been introduced into DDA, and then the key operations of solving linear equations have been analysed. Last, the calculation efficiency of various algorithms for solving linear equations are investigated through two examples of tunnelling excavation. The results show that the direct solution cannot meet the requirements of large-scale engineering computing compared with the iterative method. Although there are few differences of computing efficiency between BJ and BSOR iteration methods, both of them are obviously not as well as the PCG method. Therefore, the PCG method, in particular SSOR-PCG method is highly recommended. Jacobi-PCG is the best method to perform parallel computing, however BJ iteration is also an acceptable choice when there is an apparent inertial advantage of the stiffness matrix.

Key words: geotechnical engineering, discontinuous deformation analysis (DDA), sub-matrix technology, stiffness matrix storing, linear equations solving, block Jacobi iterative and pre-processing block conjugate gradient iteration