Cartesian perfectly matched layers for the Helmholtz equation with variable propagation speed: well-posedness and exponential convergence

We analyse the Cartesian perfectly matched layer (PML) approximation of the two-dimensional Helmholtz equation $-c^2Δu-ω^2 u=f$, in which the propagation speed $c$ is variable inside the region of interest and equal to a constant $c_\infty$ outside a disc $B_R$. Existing analyses of the Cartesian PM