Application of a time-stable model order reduction scheme to an exterior vibro-acoustic finite element model

Finite element analyses of vibro-acoustic systems are usually performed in the frequency domain, meaning that the obtained results cannot straightforwardly handle time-varying input signals. These limitations can be overcome by performing a time domain analysis of the finite element model. To reduce the calculation complexity needed for time integration a model order reduction technique is proposed. A time stable Krylov subspace reduction technique is derived for the coupled exterior vibro-acoustic problem case. The Sommer-feld radiation condition is taken into account by applying infinite elements on the boundary of the mesh. The application of time stable infinite elements leads to a potentially singular mass matrix. A method is developed that circumvents mass matrix inversion, which is based on a singular value decomposition. Combined with a special formulation of the system matrices, the proposed method is shown to preserve the stability of the full model. The resulting model order reduction procedure is applied on a numerical model of a loudspeaker.