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

09/06/2019

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by   James Bremer, et al.

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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 O(k (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.