非线性感应加热问题的全离散有限元方法

数学物理学报 ›› 2022, Vol. 42 ›› Issue (4): 1238-1255.

非线性感应加热问题的全离散有限元方法

黄媛¹,支越³,康彤^1,²,王然^1,^2,*(),张红⁴

¹ 中国传媒大学数据科学与智能媒体学院北京 100024
² 中国科学院大学计算地球动力学重点实验室北京 100049
³ 北京市育才学校通州分校北京 101101
⁴ 北京汇文中学朝阳垂杨柳分校北京 100021

收稿日期:2021-03-30 出版日期:2022-08-26 发布日期:2022-08-08
通讯作者: 王然 E-mail:wangr@ucas.ac.cn
基金资助:
国家重点研发计划项目(2020YFA0713401);国家自然科学基金项目(U2039207);国家自然科学基金项目(42074108);国家自然科学基金项目(41904067);中国传媒大学中央高校基本科研业务费专项资金

Fully Discrete Finite Element Scheme for a Nonlinear Induction Heating Problem

Yuan Huang¹,Yue Zhi³,Tong Kang^1,²,Ran Wang^1,^2,*(),Hong Zhang⁴

¹ School of Data Science and Intelligent Media, Communication University of China, Beijing 100024
² Key Laboratory of Computational Geodynamics, University of Chinese Academy of Sciences, Beijing 100049
³ Tongzhou Branch of Beijing Yucai School, Beijing 101101
⁴ Chaoyang Chuiyangliu Branch of Beijing Huiwen Middle School, Beijing 100021

Received:2021-03-30 Online:2022-08-26 Published:2022-08-08
Contact: Ran Wang E-mail:wangr@ucas.ac.cn
Supported by:
the National Key Research and Development Program of China(2020YFA0713401);the National Science Foundation of China(U2039207);the National Science Foundation of China(42074108);the National Science Foundation of China(41904067);the Fundamental Research Funds for the Central Universities

摘要/Abstract

摘要：

该文研究了一个感应加热模型, 该模型为Maxwell方程与热传导方程的耦合. 在感应加热模型中, 假设磁场与磁感应强度之间存在非线性关系, 电导率依赖于温度函数. 基于磁场H的形式, 给出时间和空间上的全离散格式, 讨论模型的可解性, 并证明全离散格式的解收敛于时间半离散的解, 而已有文献已经证明时间半离散的解收敛于连续变分问题的解. 最后, 使用数值实验去验证理论结果.

关键词: 感应加热, Maxwell方程, 非线性, 有限元, 收敛性

Abstract:

It studies an induction heating model described by Maxwell's equations coupled with a heat equation. In the induction heating model, it assumes a nonlinear relation between the magnetic field and the magnetic induction field, and the electric conductivity is temperature dependent. It presents a fully discrete H-based finite element scheme in time and space and discusses its solvability. Moreover, it proves the fully discrete solution converges to a weak solution of the continuous problem. Finally, theoretical results are supported by some numerical experiments.

Key words: Induction heating, Maxwell's equations, Nonlinear, Finite elements, Convergence

中图分类号:

O241.82

黄媛,支越,康彤,王然,张红. 非线性感应加热问题的全离散有限元方法[J]. 数学物理学报, 2022, 42(4): 1238-1255.

Yuan Huang,Yue Zhi,Tong Kang,Ran Wang,Hong Zhang. Fully Discrete Finite Element Scheme for a Nonlinear Induction Heating Problem[J]. Acta mathematica scientia,Series A, 2022, 42(4): 1238-1255.

参考文献

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