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.
Categories: math.NA cs.NA