An eigenvector‐based iterative procedure for the free‐interface component modal synthesis method

Abstract

SummaryA novel eigenvector‐based iteration procedure is developed for the free‐interface component modal synthesis (CMS) method. To derive the iteration formula, Kron's substructuring is employed to distribute the computations of subspace iteration, and the free‐interface component modes are chosen as the initial guess. Then, the modal transformation matrix of the first‐order approximated Kron's CMS method is proved to be the free‐interface component modes with one step of Kron's inverse iteration. The proposed CMS method has the advantages of both free‐interface CMS approximation and subspace iteration: on one hand, the CMS approximation provides a high‐quality initial guess and distributes the computational cost of the subspace iteration; on the other hand, the subspace iteration provides a more efficient way for truncation compensation and is compatible with using deflation, shifting, and restarting for further enhancements on the efficiency. Numerical examples show that the efficiency of the proposed method is higher than that of the conventional simultaneous iterative Kron's CMS method, especially for obtaining a large number of high‐precision modes. Moreover, the proposed method is as efficient as the global Lanczos method for first‐time analysis without parallelization while retaining the advantages of CMS methods for reanalysis tasks, parallelization, etc.