Perfectly matched layers

The simple one-dimensional steady-state acoustic problem on the domain −1 to $\mathrm{\infty }$ is solved using different acoustic elements. A source is applied at $x=-1$ of the form $u\left(-1\right)=e^{ik}$, where k is the wave number. The perfectly matched layer region is defined from 0 to 0.2 to truncate the domain. The perfectly matched layer coefficient that is used is 250. The wave number is k = 12, which gives the frequency of interest as 19.0986. The density of the acoustic medium is defined as 1, and the bulk modulus of the medium is 100. The source can be interpreted as an acoustic pressure boundary condition of 0.843853958 on the real part and −0.536572918 on the imaginary part. The end of the perfectly matched layer domain has a zero pressure boundary condition on both the real and imaginary parts.