半导体问题的交替方向有限元方法  

Alternating Direction Finite Element Method for Semiconductor Problem

作　　者：刘蕴贤[1] 

机构地区：[1]山东大学数学与系统科学学院,济南250100

出　　处：《数学物理学报（A辑）》2005年第4期433-444,共12页Acta Mathematica Scientia

基　　金：国家自然科学基金(10271066)资助

摘　　要：该文用交替方向有限元方法求解半导体问题的Energy Transport(ET)模型.对模型中椭圆型的电子位势方程采用交替方向迭代法,对流占优扩散的电子浓度和空穴浓度方程采用特征交替方向有限元方法,热传导方程利用Patch逼近采用交替方向有限元方法求解.利用微分方程的先验估计理论和技巧,分别得到了椭圆型方程和抛物型方程的最优H1和L2误差估计.The energy transport model of semiconductor problem, including both elliptic and parabolic equations, is solved by an alternating direction method. The elliptic equation for the electrostatic potential is solved by an alternating direction iterative method, the convection-dominated diffusion equations for the conservation of electron and hole concentrations are solved by an characteristic alternating direction finite element method, and the heat conduction equation is solved by an alternating direction finite element method with patch approximation. Using the theory and technique of a priori estimate of differential equation, the author obtains the optimal order error estimates in H^1-norm and L^2-norm of the elliptic equation and parabolic equations respectively.

关 键 词：半导体 交替方向 迭代 误差估计 

分 类 号：O241.82[理学—计算数学]