GaAs MESFET器件数值模拟的预优共轭梯度法

A PRE-SCALED CONJUGATE GRADIENT ALGORITHM FOR NUMERICAL SIMULATION OF MESFET PARTS

用传统的牛顿法对GaAs MESFET器件进行数值模拟,由于发散而并不成功。本文采用在不精确线性搜索条件下仍具下降性与收敛性的Fletcher-Reeves共轭梯度法,求解由非线性方程组转化成的非线性最小二乘问题。为使方法能在不同的二次区域形成共轭性较好的搜索方向,方法采用了重开始准则。为加快收敛速度,对目标函数采用了逐步预优的方法。为减少存储量,预优矩阵由Broyden修正公式产生,且不存储修正矩阵,计算结果表明方法稳定,收敛较快,数值结果与实验结果基本相符。

Abstract Newton method may diverge when used for numerical simulation of GaAs MESFET parts. A sta- ble algorithm is suggested in this paper. The algorithm employes Fletcher-Reeves' conjugate gradient method which is still descent and convergent under inexact line search, and solves the problem by translating a system of nonlinear equations into a nonlinear least squares problem. Restarting rule is used in the method so that search directions with better conjugate property may be obtained in different quadratic regions. In order to accelerate the convergence of the algorithm, objective function is regular- ly pre-scaled. The pte-scale matrix is generated by Broyden formula and does not need to be stored. An application given in the paper shows that the algorithm is stable and convergent, and that both the nu- merical and the experimental results are coincident. c