On the efficiency of the method of fundamental solutions for acoustic scattering by a poroelastic material

The Method of Fundamental Solutions is now a well established technique that has proved to be reliable for a specific range of wave problems such as the scattering of acoustic and elastic waves by obstacles and inclusions of regular shapes. The goal of this paper is to show that the technique can be extended in order to solve transmission problems whereby an incident acoustic pressure wave impinges on a poroelastic material of finite dimension. For homogeneous and isotropic materials, the wave equation for the fluid phase and solid phase displacements are found to be decoupled thanks to the Helmholtz decomposition. This allows a systematic way for obtaining an analytic expression for the fundamental solution describing the wave displacement field in the material. The efficiency of the technique relies on choosing an appropriate set of fundamental solutions as well as properly imposing the transmission conditions at the air-porous interface. In this paper, we address this issue showing results involving bidimensional scatterers of various shapes. In particular, it is shown that reliable error indicators can be used to assess the quality of the results. Comparisons with results computed using a mixed pressure-displacement finite element formulation illustrate the great advantage of this new technique both in terms of computational resources and mesh preparation.