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Investigation of highly efficient algorithms for solving linear equations in the discontinuous deformation analysis method
Author(s) -
Fu Xiaodong,
Sheng Qian,
Zhang Yonghui,
Chen Jian
Publication year - 2016
Publication title -
international journal for numerical and analytical methods in geomechanics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.419
H-Index - 91
eISSN - 1096-9853
pISSN - 0363-9061
DOI - 10.1002/nag.2407
Subject(s) - solver , conjugate gradient method , iterative method , computer science , lu decomposition , discontinuous deformation analysis , jacobi method , cuda , computational science , parallel computing , linear system , biconjugate gradient method , diagonally dominant matrix , system of linear equations , algorithm , mathematics , block matrix , linear equation , mathematical optimization , matrix decomposition , conjugate residual method , finite element method , mathematical analysis , eigenvalues and eigenvectors , gradient descent , quantum mechanics , machine learning , artificial neural network , thermodynamics , physics , pure mathematics , invertible matrix
Summary 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 © 2015 John Wiley & Sons, Ltd.