基于FFT的卷积和相关及其在求解矩形开口管道中泊松方程中的应用
On FFT-based convolutions and correlations, with application to solving Poisson's equation in an open rectangular pipe
摘要：
提出了一种求解开口矩形管内泊松方程的新方法。该方法使用快速傅里叶变换（FFT）来执行混合卷积和相关的电荷密度与格林函数。描述了基于普通格林函数和集成格林函数（IGF）的算法。由于它的相似性，广泛使用的霍克尼算法求解泊松方程在自由空间中，这种能力可以很容易地实现在许多现有的粒子在细胞束动力学代码。
英文摘要：
A new method is presented for solving Poisson's equation inside an open-ended rectangular pipe. The method uses Fast Fourier Transforms (FFTs) to perform mixed convolutions and correlations of the charge density with the Green function. Descriptions are provided for algorithms based on the ordinary Green function and for an integrated Green function (IGF). Due to its similarity to the widely used Hockney algorithm for solving Poisson's equation in free space, this capability can be easily implemented in many existing particle-in-cell beam dynamics codes.
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