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

•A fast algorithm for the 2D variable coefficient Helmholtz equation in the radially symmetric case•Allows for the solution of problems which are hundreds of thousands of wavelengths in size on desktop computers•Lays the groundwork for algorithms for the more general case of nonradially symmetric coefficients Standard solvers for the variable coefficient Helmholtz equation in two spatial dimensions have running times which grow at least 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 O(klog⁡(k)) in typical cases. We also present the results of numerical experiments demonstrating the properties of our solver, the code for which is publicly available.