MULTILEVEL AGGREGATION METHOD FOR SOLVING LARGE-SCALE GENERALIZED EIGENVALUE PROBLEMS IN STRUCTURAL DYNAMICS

In this paper a novel iterative method of multilevel type for solving large-scale generalized eigenvalue problems encountered in structural dynamics is presented. A preconditioned iterative technique, which can be viewed as a modiÞcation of the Subspace Iteration method, is used for simultaneous calculation of a group of lowest modes and frequencies. The paper demonstrates that a coarse aggregation model can be employed in the hierarchical structure of the preconditioner in order to provide a good resemblance of the latter to the sti¤ness matrix of the Þnite element approximation with respect to low-frequency modes. This leads to a fast convergent procedure of subspace iterations. As opposed to the coarse grid used in methods of multigrid type, this model allows for solving problems with di¤erent Þnite elements including reticulated structures in the framework of large comprehensive Þnite element software systems. Numerical experiments performed for three-dimensional truss, frame and solid structures demonstrate an excellent performance of the method