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《山东大学学报(理学版)》 ›› 2024, Vol. 59 ›› Issue (10): 10-21.doi: 10.6040/j.issn.1671-9352.0.2023.089

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半导体问题漂移扩散模型的超弱间断Galerkin方法

艾露露(),刘蕴贤*()   

  1. 山东大学数学学院, 山东 济南 250100
  • 收稿日期:2023-03-10 出版日期:2024-10-20 发布日期:2024-10-10
  • 通讯作者: 刘蕴贤 E-mail:1124551490@qq.com;yxliu@sdu.edu.cn
  • 作者简介:艾露露(1999—), 女, 硕士, 研究方向为偏微分方程数值解. E-mail: 1124551490@qq.com
  • 基金资助:
    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)

An ultra-weak discontinuous Galerkin method for drift-diffusion model of semiconductor problem

Lulu AI(),Yunxian LIU*()   

  1. School of Mathematics, Shandong University, Jinan 250100, Shandong, China
  • Received:2023-03-10 Online:2024-10-20 Published:2024-10-10
  • Contact: Yunxian LIU E-mail:1124551490@qq.com;yxliu@sdu.edu.cn

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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。

关键词: 漂移扩散模型, 超弱间断Galerkin方法, 误差分析, 数值模拟

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. Compared to the local discontinuous Galerkin method, this method can solve partial differential equations with higher-order spatial derivatives 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.

Key words: drift-diffusion model, ultra-weak discontinuous Galerkin method, error analysis, numerical simulation

中图分类号: 

  • O241.82

图1

UWDG方法和LDG方法下的数值模拟在稳态时的结果"

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