Investigation of highly efficient algorithms for solving linear equations in the discontinuous deformation analysis method

Large-scale engineering computing using the discontinuous deformation analysis (DDA) method is time-consuming, which hinders the application of the DDA method. The simulation result of a typical numerical example indicates that the linear equation solver is a key factor that affects the efficiency of the DDA method. In this paper, highly efficient algorithms for solving linear equations are investigated, and two modifications of the DDA programme are presented. The first modification is a linear equation solver with high efficiency. The block Jacobi (BJ) iterative method and the block conjugate gradient with Jacobi pre-processing (Jacobi-PCG) iterative method are introduced, and the key operations are detailed, including the matrix-vector product and the diagonal matrix inversion. Another modification consists of a parallel linear equation solver, which is separately constructed based on the multi-thread and CPU-GPU heterogeneous platforms with OpenMP and CUDA, respectively. The simulation results from several numerical examples using the modified DDA programme demonstrate that the Jacobi-PCG is a better iterative method for large-scale engineering computing and that adoptive parallel strategies can greatly enhance computational efficiency. Copyright (c) 2015 John Wiley & Sons, Ltd.