Proper Generalized Decomposition applied to linear acoustic: A new tool for broad band calculation

The calculation of the acoustic response of systems in frequency bands is becoming increasingly important in simulation-based engineering design. This is particularly true in medium-frequency bands, where the response is very sensitive to the frequency. Some standard techniques for addressing these problems present a frequency dependent formulation and may involve fixed-frequency calculations at many different frequencies. In this paper, we propose a new technique which combines the Variational Theory of Complex Rays (VTCR) with Proper Generalized Decomposition (PGD) and does not require the resolution of acoustic problems at many frequencies. In this approach, the VTCR is used to find an approximate solution of a medium-frequency acoustic problem using only a few degrees of freedom (DOFs). Then, PGD is used to find a representation of the approximate solution which is separated between two variables, the wave propagation direction and the frequency. A relevant numerical example is used to present the strategy and illustrate its applicability for frequency band calculations.