A Spectral Method For The Helmholtz Equation In Unbounded Domain With Perfectly Matched Layer

The Helmholtz equation describes a wide variety of wave propagation phenomena including electromagnetic waves and acoustics. We consider the two-dimensional Helmholtz equation in a semi-infinite strip domain, and apply the technique of perfectly matched layer (PML) to transform the infinite domain to a finite one. We propose a spectral method to the Helmholtz-PML problem and discuss the impact of the PML parameters on the accuracy of the numerical solution.This paper consists of several parts. In the first part, we attempt to provide a brief review on the Helmholtz equation. The second part of this paper contributes to applying the PML method to transform the problem on infinite domain to a bounded one. In the third part we approximate the Helmholtz-PML problem by a spectral method and discuss the impact of the PML parameters on the accuracy of the numerical solution. Finally, some numerical experiments are performed to confirm our analysis.