模拟热电半导体器件的保守数值算法与无条件最佳收敛分析

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications Pub Date : 2024-09-12 DOI:10.1016/j.camwa.2024.09.002

Xindong Li, Wenwen Xu

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引用次数: 0

摘要

我们提出了模拟半导体热电器件问题的保守型数值方法，其中电势方程采用混合有限元法，电子和空穴浓度方程采用保守特征有限元法，热传导方程采用标准有限元法。通过时空误差分割论证，得出了无一定时间步长限制的最优误差估计值，且静电势和电场强度的低阶收敛速率不会影响电子、空穴密度和温度的精度。通过数值测试验证了所给方法的理论结果和应用性能。

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Conservative numerical algorithm for simulating thermoelectrical semiconductor device with unconditional optimal convergence analysis

We propose conservative type numerical method to simulate thermoelectrical semiconductor device problem, in which mixed finite element method used for electric potential equation, conservative characteristic finite element method for electron and hole concentration equations, and standard finite element method for heat conduction equation. By temporal-spatial error splitting argument, the optimal error estimates without certain time step restriction are derived, and low order convergence rate of electrostatic potential and electric field intensity will not affect the accuracy of the electron, hole density and temperature. Numerical tests are performed to validate the theoretical results and application performance of the given method.

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来源期刊

Computers & Mathematics with Applications 工程技术-计算机：跨学科应用

CiteScore

5.10

自引率

10.30%

发文量

396

审稿时长

9.9 weeks

期刊介绍： Computers & Mathematics with Applications provides a medium of exchange for those engaged in fields contributing to building successful simulations for science and engineering using Partial Differential Equations (PDEs).