Analysis of a Cartesian PML approximation to acoustic scattering problems in \(\mathbb R^2\) and \(\mathbb R^3\)
This paper deals with the exterior Helmholtz scattering problem \[ \Delta u+ k^2u= 0\quad\text{in }\Omega^c,\;u= g\quad\text{on }\Gamma=\partial\Omega^c, \] \[ \lim_{r\to\infty} r^{(n-1)/2} \Biggl({\partial u\over\partial r}- iku\Biggr)= 0. \] Here \(\Omega\) is a bounded domain in \(\mathbb{R}^n\), \(n= 2,3\), and \(\Omega^c\) denotes the complement of its closure. The limit is taken to mean uniformly on the sphere of radius \(r\). The authors use a perfectly matched layer (PML) technique based on Cartesian geometry where each variable is transformed independently to approximate solutions. Some results of numerical calculations which illustrate the convergence behavior of the PML approximations are presented.
scientific article; zbMATH DE number 6155449