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Analysis of a two-grid method for semiconductor device problem

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Abstract

The mathematical model of a semiconductor device is governed by a system of quasi-linear partial differential equations. The electric potential equation is approximated by a mixed finite element method, and the concentration equations are approximated by a standard Galerkin method. We estimate the error of the numerical solutions in the sense of the Lq norm. To linearize the full discrete scheme of the problem, we present an efficient two-grid method based on the idea of Newton iteration. The main procedures are to solve the small scaled nonlinear equations on the coarse grid and then deal with the linear equations on the fine grid. Error estimation for the two-grid solutions is analyzed in detail. It is shown that this method still achieves asymptotically optimal approximations as long as a mesh size satisfies H = O(h1/2). Numerical experiments are given to illustrate the efficiency of the two-grid method.

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Authors and Affiliations

  1. School of Mathematics and Computational Science, Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University, Xiangtan, Hunan Province, 411105, China

    Ying Liu, Yunqing Huang & Qingfeng Li

  2. College of Information and Intelligence, Hunan Agricultural University, Changsha, 410128, China

    Ying Liu

  3. School of Mathematical Sciences, South China Normal University, Guangzhou, 510631, China

    Yanping Chen

Authors
  1. Ying Liu
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  2. Yanping Chen
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  3. Yunqing Huang
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  4. Qingfeng Li
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Corresponding author

Correspondence to Yanping Chen.

Additional information

Project supported by the State Key Program of National Natural Science Foundation of China (No. 11931003) and the National Natural Science Foundation of China (Nos. 41974133, 11671157, and 11971410)

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Liu, Y., Chen, Y., Huang, Y. et al. Analysis of a two-grid method for semiconductor device problem. Appl. Math. Mech.-Engl. Ed. 42, 143–158 (2021). https://doi.org/10.1007/s10483-021-2696-5

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  • DOI: https://doi.org/10.1007/s10483-021-2696-5

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Chinese Library Classification

2010 Mathematics Subject Classification

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