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.