A Uniaxial Optimal Perfectly Matched Layer Method for Time-Harmonic Scattering Problems

Abstract

We develop a uniaxial optimal perfectly matched layer (opt PML) method for solving the time-harmonic scattering problems by choosing a particular absorbing function with unbounded integral in a rectangular domain. With this choice, the solution of the optimal PML problem not only converges exponentially to the solution of the original scatting problem, but also is insensitive to the thickness of the PML layer for sufficiently small parameter $ε_0$. Numerical experiments are included to illustrate the competitive behavior of the proposed optimal method.