泊松方程数值解法的加速收敛法

The Accelerating Convergence Method for the Numerical Solution of Poisson's Equation

用数值方法对泊松方程求解时,往往要对迭代的中间结果作适当的压缩处理,以加快收敛速度和避免溢出.本文提出一种单一指数因子的非线性压缩法.一维数值模拟结果表明,平衡态时不必进行压缩处理.而在非平衡态时,最佳指数压缩因子的大小与杂质浓度有关.参考本文给出的数值计算结果,根据给定器件的杂质浓度分布,选定一最佳指数压缩因子,可以使泊松方程的数值求解过程具有最决的收敛速度.

When the numerical method is used to solve poisson's equation, middle results in the iteration are damped advisably in order to accelerate the speed of convergence and avoid overflow. A form of non-linearity damping is reported in the paper. The one-dim(?)ntional numerical results show that the damping is not necessary in the equilibrium stat(?), and the best exponential factor of damping is dependent on the dopant density in the non(?)quilibrium state. Refering to the numerical results represented in this paper and selecting the best exponential factor of damping for the dopant density of a given device, we can obtain the fastest speed of convergence to solve Posson's equation with the numerical method.