Analysis of a Cartesian PML approximation to acoustic scattering problems in R2

In this paper, we consider a Cartesian PML approximation to solutions of acoustic scattering problems on an unbounded domain in R2. The perfectly matched layer (PML) technique in a curvilinear coordinate system has been researched for acoustic scattering applications both in theory and computation. Our goal will be to extend the results of spherical/cylindrical PML to PML in Cartesian coordinates, that is, the well-posedness of Cartesian PML approximation on both the unbounded and truncated domains. The exponential convergence of approximate solutions as a function of domain size is also shown. We note that once the stability and convergence of the (continuous) truncated problem has been achieved, the analysis of the resulting finite element approximations is then classical. Finally, the results of numerical computations illustrating the theory and efficiency of the Cartesian PML approach will be given.