Perfectly matched layers for the numerical approximation of the radiation boundary condition in structural acoustic finite element tools

Abstract

The Berenger perfectly matched layer (PML) is one of a variety of numerical techniques for approximating the Sommerfeld radiation boundary condition. In acoustics, the PML is a nonphysical finite thickness layer of fluid or solid material that surrounds the physical computational domain of interest and acts as an anisotropic absorber of the outgoing waves. The absorption coefficients in the PML are such that the acoustic energy is dissipated selectively only in the direction perpendicular to the interface between the PML and the physical domain. The study presented here shows that the appropriate choice of PML absorbing functions can have a beneficial effect on the convergence of frequency domain acoustic finite-element tools. In the context of elastic target scattering computations, it is shown how the PML can be applied in direct contact with the wet surface of convex elastic targets. Other examples from low-frequency geoacoustic benchmarking applications demonstrate the adaptability of the PML to a variety of geometries and to problems where the radiation condition must be imposed across inhomogenous layers. The numerical results obtained with the finite-element/PML tool are compared to results from finite-element/infinite-element codes and to results from parabolic equation models.