We consider a wide variety of scattering problems including scattering by Dirichlet, Neumann, and penetrable obstacles. We consider a radial perfectly-matched layer (PML) and show that for any PML width and a steep-enough scaling angle, the PML solution is exponentially close, both in frequency and the tangent of the scaling angle, to the true scattering solution. Moreover, for a fixed scaling angle and large enough PML width, the PML solution is exponentially close to the true scattering solution in both frequency and the PML width. In fact, the exponential bound holds with rate of decay $c(w\tan\theta -C) k$ where $w$ is the PML width and $\theta$ is the scaling angle. More generally, the results of the paper hold in the framework of black-box scattering under the assumption of an exponential bound on the norm of the cutoff resolvent, thus including problems with strong trapping. These are the first results on the exponential accuracy of PML at high-frequency with non-trivial scatterers.

翻译：我们考虑了各种各样的散射问题,包括Drichlet、Neumann和穿透屏障的散射问题。我们考虑的是完全匹配的辐射层(PML),并表明对于任何PML宽度和陡度缩放角度,PML溶液在频率和伸缩角度上都成倍接近真正的散射方法;此外,对于固定的缩放角度和足够大的PML宽度,PML溶液在频率和PML宽度上都指数接近真正的散射解决办法。事实上,指数约束值与美元(w\tan\theta-C) k$(美元是PML宽度)和美元($\theta) k$(美元)是缩放角度。更一般地说,在黑盒散射框架内的纸屏蔽结果假定在截断点的规范上是指数捆绑,从而包括强陷阱问题。这些是高频点与非三分散射器的PML指数精确度的第一个结果。