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 $\mathcal{O}(k\log (k))$ in typical cases. We also present the results of numerical experiments demonstrating the properties of our solver, the code for which is publicly available.

中文翻译：

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二维径向对称电势散射数值模拟的拟线性复杂度算法

二维空间中变系数Helmholtz方程的标准求解器的运行时间至少随波数k二次方增长。在这里，我们描述一种求解器，该求解器仅在散射势为径向对称但运行时间为$\mathcal{Ø}（ķ\mathrm{日志}（ķ））$在典型情况下。我们还提供了数值实验的结果，这些结果证明了求解器的性能，该求解器的代码可公开获得。