基于非均匀FFT的非局部势新求解器：用于Davey-Stewartson方程高效模拟
A novel nonlocal potential solver based on nonuniform FFT for efficient simulation of the Davey-Stewartson equations
AI总结：
本文提出一种基于非均匀FFT的非局部势求解器，用于高效求解Davey-Stewartson方程。通过消除极坐标中的不连续性，将积分拆分为高频和低频部分，利用非均匀FFT加速高阶高斯求积，实现O(N log N)复杂度和更高精度。
摘要：
我们提出了一种高效的非局部势求解器，用于Davey-Stewartson方程。非局部势的傅里叶变换中的不连续性会导致标准FFT在截断域上出现精度锁定问题。利用极坐标中不连续性消失的特性，我们将势积分重新公式化并拆分为高频和低频部分。高频部分可通过标准FFT方法近似，而低频部分则通过非均匀FFT加速的高阶高斯求积进行计算。非均匀FFT求解器具有O(N log N)的复杂度，其中N是离散化点的总数，并在精度上优于标准FFT求解器，使其成为模拟的优良替代方案。大量数值结果展示了所提方法的效率和精度。
英文摘要：
We propose an efficient and accurate solver for the nonlocal potential in the Davey-Stewartson equation using nonuniform FFT (NUFFT). A discontinuity in the Fourier transform of the nonlocal potential causes accuracy locking if the potential is solved by standard FFT with periodic boundary conditions on a truncated domain. Using the fact that the discontinuity disappears in polar coordinates, we reformulate the potential integral and split it into high and low frequency parts. The high frequency part can be approximated by the standard FFT method, while the low frequency part is evaluated with a high order Gauss quadrature accelerated by nonuniform FFT. The NUFFT solver has $O(N\log N)$ complexity, where $N$ is the total number of discretization points, and achieves higher accuracy than standard FFT solver, which makes it a good alternative in simulation. Extensive numerical results show the efficiency and accuracy of the proposed method.
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