半导体问题漂移扩散模型的超弱间断Galerkin方法
An ultra-weak discontinuous Galerkin method for drift-diffusion model of semiconductor problem
艾露露 1刘蕴贤1
作者信息
- 1. 山东大学数学学院,山东济南 250100
- 折叠
摘要
利用超弱间断Galerkin(ultra-weak discontinuous Galerkin,UWDG)方法对一维半导体漂移扩散模型进行数值模拟,并给出了误差分析.该方法具有经典间断Galerkin方法的优点.相较于局部间断Galerkin方法,它在求解含高阶空间导数的偏微分方程时,可以不引入辅助变量,在结构上更简单,在计算上更直接.主要技术困难在于选取合适的投影对方法进行误差估计.数值模拟的结果验证了 UWDG方法的稳定性.
Abstract
An ultra-weak discontinuous Galerkin(UWDG)method is developed for the drift-diffusion model of the semiconductor problem with the error analysis.The UWDG method has the advantage of the classical discontinuous Galerkin(DG)method.Com-pared to the local discontinuous Galerkin method,this method can solve partial differential equations with higher-order spatial deriva-tives without introducing auxiliary variables,which is simpler in scheme and more direct in calculation.The main technical difficulty is to select the appropriate projection for error analysis.A numerical simulation is performed to validate the numerical stability of the UWDG method.
关键词
漂移扩散模型/超弱间断Galerkin方法/误差分析/数值模拟Key words
drift-diffusion model/ultra-weak discontinuous Galerkin method/error analysis/numerical simulation引用本文复制引用
基金项目
国家自然科学基金资助项目(12071262)
山东省自然科学基金资助项目(ZR201911130593)
山东省自然科学基金资助项目(ZR2020MA048)
出版年
2024
NETL
NSTL
万方数据