Premium
Comparison of Preconditioned Conjugate Gradient Method and LDL T Factorization for Structural Analysis
Author(s) -
Suarjana Made
Publication year - 1998
Publication title -
computer‐aided civil and infrastructure engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.773
H-Index - 82
eISSN - 1467-8667
pISSN - 1093-9687
DOI - 10.1111/0885-9507.00107
Subject(s) - conjugate gradient method , incomplete cholesky factorization , factorization , conjugate , linear system , sparse matrix , range (aeronautics) , matrix decomposition , computer science , system of linear equations , matrix (chemical analysis) , mathematics , incomplete lu factorization , lu decomposition , conjugate residual method , algorithm , mathematical optimization , mathematical analysis , gradient descent , physics , chemistry , materials science , chromatography , eigenvalues and eigenvectors , quantum mechanics , machine learning , artificial neural network , composite material , gaussian
This paper compares the efficiency of the preconditioned conjugate gradient (PCG) method and the LDL T factorization for solving a sparse system of linear equations in large‐scale structural analysis with both single‐ and multiple‐load cases. In the PCG method we present an incomplete LDL T preconditioning method that can be used to efficiently solve a system of linear equations with a wide range of matrix conditions, system sizes, and computer memory limitations. The preconditioning method is very flexible, and we can easily balance the size of the preconditioning matrix and the level of the preconditioning that is appropriate for the problem to be solved. For comparison, we use an implementation of a row‐oriented sparse LDL T solution method.