A delayed frequency preconditioner approach for speeding-up frequency response computation of structural components

In this work, a delayed frequency preconditioner (DFP) is developed and applied in structural problems for speeding-up the frequency response computation. The challenge of computing the frequency response lies in the computation of the linear system that involves the excitation forces and also the dynamic stiffness which is frequency-dependent. For each frequency, the dynamic stiffness must be updated and a new factorization must be performed, which introduces a high computational cost on the solutions of the linear systems. Alternatively, iterative solver such as GMRES can be applied to avoid the cost of factorization, however they require good preconditioners that are traditionally also frequency-dependent. In the new approach, the dynamic stiffness operator is updated with the frequency whereas the preconditioner is kept constant for a range of frequencies serving as a low-cost preconditioner for the iterative solver. This technique saves computation time because a new factorization is avoided for each frequency point. On the other hand, the effectiveness of the delayed preconditioner is destroyed when the frequency of the dynamic operator is too far away from each other. Therefore, we propose a heuristic approach to update the preconditioner when it is underperforming. The algorithm is tested on structural problems and the results show that this approach can drastically reduce the number of iterations for the computation of the frequency response.