| 三维热传导型半导体器件瞬态模拟问题的Crank-Nicolson差分-流线扩散有限元法及其数值分析 |
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| 引用本文： | 张争茹,羊丹平.三维热传导型半导体器件瞬态模拟问题的Crank-Nicolson差分-流线扩散有限元法及其数值分析[J].应用数学学报,2002,25(2):230-243. |
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| 作者姓名： | 张争茹 羊丹平 |
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| 作者单位： | 山东大学数学系,济南,250100 |
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| 基金项目： | 国家重点基础研究规划项目（G1999032803），教育部高等院校骨干教师专项科研基金资助项目. |
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| 摘 要： | 本文研究三维热传导型半导体器件瞬态模拟问题的数值方法.针对数学模型中各方程不同的特点,分别提出不同的有限元格式.特别针对浓度方程组是对流为主扩散问题的特点,使用Crank-Nicolson差分-流线扩散计算格式,提高了数值解的稳定性.得到的L2误差估计关于空间剖分步长是拟最优的,关于时间步长具有二阶精度.
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| 关 键 词： | 半导体 三维热传导 Crank-Nicolson格式 差分流线扩散法 误差估计 |
| 修稿时间： | 2000年1月28日 |
C-N DIFFERENCE STREAMLINE DIFFUSION METHOD FOR THREE-DIMENSIONAL SEMICONDUCTOR PROBLEM WITH HEAT-CONDUCTION AND NUMERICAL ANALYSIS |
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| ZHANG ZHENGRU,YANG DANPING.C-N DIFFERENCE STREAMLINE DIFFUSION METHOD FOR THREE-DIMENSIONAL SEMICONDUCTOR PROBLEM WITH HEAT-CONDUCTION AND NUMERICAL ANALYSIS[J].Acta Mathematicae Applicatae Sinica,2002,25(2):230-243. |
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| Authors: | ZHANG ZHENGRU YANG DANPING |
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| Abstract: | Abstract In this article, we study the numerical method for simulation of three-dimensional semiconductor problem with heat-conduction. Considering different types of partial differential equations arising from the model for the transient behavior of a semiconductor device, we present different finite element scheme respectively. Especially, we use Crank-Nicolson difference streamline diffusion method to treat convection-diffusion equations of the concentrations of electron and hole in the model. The numerical stability is improved by difference streamline diffusion method. An error estimate in L2 norm with quasi-optimal accuracy in space and second order accuracy in time is derived. |
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| Keywords: | Three-dimensional heat conduction semiconductor C-N scheme difference streamline diffusion method error estimate |
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