一种高效的旋转体散射问题求解器
An efficient solver for problems of scattering by bodies of revolution
AI总结：
本文提出一种基于加法定理和快速勒让德变换的迭代求解器，以$O(N\log^2 N)$复杂度求解轴对称散射问题，对光滑介质具有谱精度。
摘要：
本提案涉及一种用于求解轴对称散射问题的新型数值方案的设计、分析与应用。为此，引入了一种迭代求解Lippmann-Schwinger积分方程的程序，其计算复杂度为$O(N\log^2 N)$，其中$N$为离散点数。该方法通过使用加法定理和快速勒让德变换（FLT）实现了高效性。对于全局光滑的声速/折射率，该方法具有谱精度。更一般地，收敛阶与解的光滑性相关，并且实际上受限于解的光滑性。
英文摘要：
This proposal relates to the design, analysis and application of a novel numerical scheme for the solution of axisymmetric scattering problems. To this end, a procedure is introduced to iteratively evaluate the solution of the Lippmann-Schwinger integral equation in $O(N\log^2 N)$ operations, where $N$ is the number of the discretization points. The method achieves its efficiency through the use of the addition theorem and Fast Legendre Transforms (FLT). For globally smooth sound velocities/refractive indexes the method is spectrally accurate. More generally the order of convergence is tied to and in fact, limited by, the smoothness of the solution.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
