Efficient Sound Power Computation of Open Structures With Infinite/Finite Elements and by Means of the Padé-via-Lanczos Algorithm

The solution of time-harmonic acoustic problems suffers from a frequency dependency which usually requires to solve the systems for many discrete frequencies independently. Among others, the Padé-via-Lanczos approximation provides an efficient solution. Herein, this method is applied to the external acoustic problem by using a finite and infinite element formulation. The state-space system matrix is first reduced to a condensed transfer matrix which is approximated in a power series, i.e. Padé approximation. The coefficients of this power series are reconstructed by using a Krylov basis, i.e. Lanczos method. Based on this method, the authors provide a formulation for the radiated sound power. The necessary integration over the boundary for the sound power is done in the first vectors of the Lanczos method. Thus the scalar sound power can be approximated in a certain frequency band by means of a transfer matrix, which is several orders of magnitude smaller than the total numbers of degrees of freedom of the overall problem. The error of this additional approximation can be estimated. The method is tested in an example of an open cavity including two loadcases, one representing a cavity with an open window, the other one being a radiating obstacle.