The preconditioned conjugate gradient method with incomplete factorization preconditioners

We present a modification of the ILUT algorithm due to Y. Saad for preparing incomplete factorization preconditioner for positive definite matrices being neither diagonally dominant nor M-matrices. In all tested cases, the rate of convergence of the relevant preconditioned conjugate gradient method was at a sufficient level, when linear systems arising from static problem for bar structures with 3D beam elements were solved.