JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2024, Vol. 59 ›› Issue (10): 10-21.doi: 10.6040/j.issn.1671-9352.0.2023.089

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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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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

CLC Number: 

  • O241.82

Fig.1

The numerical simulation results of the UWDG method and LDG method at steady state"

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