A spectrally preconditioned iterative reduced correction algorithm for vibro-acoustic problems

Abstract

A new iterative method for the prediction of dynamic characteristics of coupled vibro-acoustic systems is presented in this study. The proposed method extracts the eigenvectors in a specified frequency band and it is similar in concept to the well-known eigenvalue solvers, such as the Lanczos method. At each iteration step a reduction subspace is built and the problem is projected onto this subspace which is built up from a combination of the so-called correction vectors and the uncoupled modes. The correction vectors are used to correct the starting uncoupled modes of the coupled physics. In the iterations, the uncoupled modes, correction vectors and frequencies are updated. Correction vectors are found by the use of an iterative solution method. Namely, the conjugate gradient method is used along with spectral expansion properties of the matrices to end up with an extremely efficient preconditioner. However, to save some computational cost, an iteration limit is used for the iterative solution process. These vectors are shown to enrich the reduction space in an iterative sense. Concerning the developed method, some test applications are provided. © The Society for Experimental Mechanics, Inc. 2012.