Efficient multi-frequency solutions of FE–BE coupled structural–acoustic problems using Arnoldi-based dimension reduction approach

The frequency sweep analysis is indispensable for the performance prediction and optimization design of structural–acoustic interaction problems. The coupled finite element and boundary element (FE–BE) method has been widely used to perform such simulations. However, the straightforward solution of the resulting hybrid model for a large number of frequencies is computationally prohibitive due to the unfavorable properties of involved matrices, e.g. large-scale, non-symmetric and especially frequency-dependent. In order to ease this challenge, a three-step structure-preserving model order reduction method is presented, which is based on an offline-online computing framework. As a first step, the second-order Arnoldi process is used to speed up calculations of the sparse structural part of the strongly coupled system. In a second step, the low-dimensional approximations of the FE unknown variables are eliminated from the global system of equations and after that the remaining dense BE degrees of freedom are reduced by application of the standard Arnoldi-based Krylov subspace algorithm. A transformation technique based on Taylor's theorem is incorporated to decouple the frequency from the Green's function and a column-by-column low-memory projection is further sought to favor the overall storage requirements. In the last step, a robust reduced order model can be quickly retrieved by simple algebraic manipulations, which allows a direct solver without any costly matrix operation to be used for the online sweeps, requiring only a very small fraction of the total CPU runtime. Two numerical cases are investigated to highlight the potential of the proposed approach in multi-frequency applications.