A quasilinear complexity algorithm for the numerical simulation of scattering from a two-dimensional radially symmetric potential

Abstract

Standard solvers for the variable coefficient Helmholtz equation in two spatial dimensions have running times which grow quadratically with the wavenumber $k$. Here, we describe a solver which applies only when the scattering potential is radially symmetric but whose running time is $\mathcal{O}\left(k\log (k)\right)$ in typical cases. We also present the results of numerical experiments demonstrating the properties of our solver, the code for which is publicly available.