An analytical study of the discrete perfectly matched layer for the time-domain Maxwell equations in cylindrical coordinates

We present an analysis of the perfectly matched layer in cylindrical coordinates discretized with a staggered second-order accurate finite difference time domain method. For fixed discretization parameters, layer width, and a quadratic loss function, we find the numerical reflection produced by the discrete layer is accurately predicted by the infinite resolution reflection coefficient for sigma(max) is an element of [0, sigma(max)(c)], where sigma(max) is the maximum value of the absorption parameter in the layer. We also find that the finite resolution reflection coefficient achieves its minimum value at sigma(max)(m) > sigma(max)(c). Numerical experiments validate the analysis.