Performance Improvement Algorithm for Mode-Based Frequency Response Analysis

A new algorithm that reduces the cost of mode-based frequency response analysis is presented. The algorithm takes advantage of the algebraic structure of the linear systems of equations for the frequency response analysis in a modal subspace and transforms the system to reduce the cost of factorizing the left-hand side operator. The transformed system is equivalent to the original one; thus, the proposed algorithm does not affect the accuracy of the solution. It can be derived that this algorithm reduces the cost of the analysis by a factor of about 2, regardless of the size of the problem. This algorithm can be generalized for the case of the coupled structural-acoustic frequency response analysis.