A fast direct solver for non-intrusive reduced order modeling of vibroacoustic problems

Abstract

This paper proposes a fast model order reduction method for large-scale three-dimensional vibro-acoustic coupling problems, which proceeds in three perspectives. Firstly, part of the coupling matrices is neglected and another part of the coupling matrices is treated as the partial right-hand side of the Schur complement of the corresponding subsystem in order to implement model reduction quickly. Secondly, the proposed fast method does not require the use of the underlying complex-valued and dense boundary element full-order model for the construction of a global orthonormal basis in the offline phase. Rather, its sparse approximation is exploited, which benefits from the consistent amplitude decay property of the kernel functions. This way it can be regarded as a non-intrusive method. Lastly, in addition to structural loads, acoustic loads, such as the load from incident waves impinging on the flexible structure from the outside, can be handled as well. Application of this solution method to the frequency sweep analyses of coupled structural acoustic systems, i.e. simple sphere and complex geometrical model submerged in an infinite fluid with the number of degrees of freedom ranging from hundreds of thousands up to millions, shows the improved computational efficiency and reduced memory requirement as compared to the brute force approach based on the direct evaluation of original high-dimensional models and also the previous acceleration scheme.