Block preconditioned conjugate gradient method for extraction of natural vibration frequencies in structural analysis

The block preconditioned conjugate gradient method for extraction of eigenfrequencies and eigenmodes is presented for finite element software in structural analysis. The proposed approach is focused on multi-core desktops and laptops and allows us to effectively analyze large design models, when classical methods based on the factoring of stiffness matrix, significantly reduce performance by intensive use of disk memory. The main attention is paid to proper construction of preconditioning, application of shift technique and creation of the block algorithm allowing the improvement of computing stability and multithreaded parallelization.