A Uniaxial Optimal Perfectly Matched Layer Method for Time-Harmonic Scattering Problems (Communications in Mathematical Research, 2021)
We develop a uniaxial optimal perfectly matched layer (opt PML) methodfor solving the time-harmonic scattering problems by choosing a particular absorbingfunction with unbounded integral in a rectangular domain. With this choice, thesolution of the optimal PML problem not only converges exponentially to the solutionof the original scatting problem, but also is insensitive to the thickness of the PMLlayer for sufficiently small parameter $ε_0$. Numerical experiments are included toillustrate the competitive behavior of the proposed optimal method.