基于化学物质释放的五点傅里叶变换求解泊松方程的方法

在电离层化学物质释放数值模拟中，傅里叶变换是一种有效的求解泊松方程的方法，但其仿真精度有待进一步提高.文章提出一种改进的傅里叶变换求解泊松方程的方法，对泊松方程的五点差分形式做傅里叶变换，并引入误差修正项，弥补二阶差分带来的误差，模型中给出了详细推导过程，并与常用方法进行了对比分析.研究结果表明，改进方法求得电势的均方误差（Mean Square Error，MSE）相对Birdsall方法和电势求导方法小6个量级，电势空间分布更加接近解析结果.文中所提方法满足化学物质释放数值仿真的要求，为等离子体粒子模拟中泊松方程的求解提供了一种新的方法.

Five point Fourier transform method for solving Poisson equation based on chemical release

Flourier transform method is an effective method for solving Poisson equation in the numerical simulation of chemical release in the ionosphere,but the simulation accuracy needs to be improved.An improved method of Fourier transform to solve the Poisson equation is proposed.This method takes a Fourier transformation of the five point difference form of the Poisson equation and introduces an error correction term to make up the errors caused by the two order difference.The paper gives the detailed derivation process,and compares the improved method with the other methods.The result indicates that the mean square error of potential obtained by the improved method is 6 orders of magnitude less than the Birdsall methods and the potential derivative method,and the spatial distribution of the potential is closer to the analytical result.The proposed method meets the requirement of numerical simulation of chemical release in the ionosphere,and it provides a new method for solving Poisson equation in plasma particle simulation.