A Coupled Finite Element–Wave Based Approach for the Steady-State Dynamic Analysis of Acoustic Systems

Abstract

The finite element method (FEM) is widely accepted for the steady-state dynamic response analysis of acoustic systems. It exhibits almost no restrictions with respect to the geometrical features of these systems. However, it is limited to the low-frequency range due to the rapidly growing model size for increasing frequencies. An alternative method is the wave based method (WBM), which is based on the indirect Trefftz approach. It exhibits better convergence properties than the FEM and therefore allows accurate predictions at higher frequencies. However, the applicability is limited, since the high computational efficiency only appears for systems of moderate geometrical complexity. In order to benefit from the advantageous features of both methods, i.e. the wide application range of the FEM and the high convergence rate of the WBM, the coupling between both methods is proposed. Only the parts of the problem domain with a complex geometry are modeled using the FEM, while the remaining parts are described with a wave based model. The resulting hybrid model contains less degrees of freedom, which allows a further model refinement. The proposed coupled approach has the potential to cover the mid-frequency range, where it is still difficult to obtain satisfactory prediction results with currently existing deterministic techniques.