Perfectly matched layers

Abstract

This is a survey of some recent developments on the so called Perfectly Matched Layer (PML) method. We take as model the scattering problems in linear acoustics. First, the Cartesian PML equations are described in the time domain for the split Berenger and the unsplit Zhao-Cangellaris formulations. The energy estimates existing in the literature are revised, and the coupled fluid/PML problem is introduced. Next, the pressure formulation of the Cartesian PML model is derived in the frequency domain. We show that a PML method based on a non-integrable absorbing function allows recovering the exact solution in the physical domain of interest, in the framework of plane waves with oblique incidence. We revise the theoretical results that state the well-posedness of the continuous model for the acoustic scattering problem. Finally, we illustrate with some numerical results the efficiency and accuracy of the Cartesian PML approach and compare different absorbing profiles. Finally, we introduce the pressure formulation of the radial PML model in the frequency domain and revise the theoretical results that assess the accuracy of this technique in the continuous model. Under convenient assumptions, we show its convergence when the thickness of the PML becomes larger and its exactness when a non-integrable absorbing function is used. The numerical accuracy of this approach is also illustrated. © 2008 Springer-Verlag.