An absorbing matched layer implementation for the transmission line matrix method

An absorbing matched layer for the Transmission Line Matrix method in acoustics is proposed. So far, existing formulations of absorbing layers for TLM have been obtained from empirical considerations. In the present study, a formulation is proposed on the basis of acoustic equations. The approach is based on the discretization of the propagation wave equation for a dissipative and non-homogeneous medium and from the Perfectly Match Layer formalism of Bérenger. Two solutions are proposed that both give a specific scattering matrix for the Transmission Line Matrix method: one is equivalent to an artificial purely dissipative medium and the other to a non-homogeneous and dissipative artificial medium. The proposed solutions are compared to an existing empirical formulation of absorbing layer. It is shown that the non-homogenous and dissipative solution is less interesting than the purely dissipative one because its efficiency can strongly depend on the receiver location. The purely dissipative solution can outperform the empirical matched connexion law formulation for a large range of incidence angle if an optimized value of the damping factor is used. For the frequency 100 Hz, significant efficiencies better than 28 dB for normal to grazing incidence, and between 30 dB and 50 dB for normal incidence to oblique incidence can be reached, with an absorbing layer thickness of only one wavelength.