Comparison of Preconditioned Conjugate Gradient Method and LDLT Factorization for Structural Analysis

Abstract

This paper compares the efficiency of the preconditioned conjugate gradient (PCG) method and the LDLTfactorization 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 LDLT 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 LDLT solution method.