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对静电场电势求解的有限差分法和逐次超松弛迭代法的研究
发表时间：2021-01-08 浏览量：1313 下载量：212
| 全部作者： | 孙浩，朱笑莹，王诗 |
| 作者单位： | 辽宁工程技术大学电子与信息工程学院 |
| 摘 要： | 通过有限差分法求得静态场的差分方程组，利用超松弛迭代法求解差分方程组，可以得到静态场的近似解。本文以静态场的求解问题为例，利用Python编写程序并绘制图像，验证了此方法的正确性。同时，研究了逐次超松弛迭代法中迭代次数对误差的影响以及逐次超松弛迭代法中最优松弛因子与有限差分法中网格密度的关系，为有限差分法和逐次超松弛迭代法在工程问题中的应用提供科学参考。 |
| 关 键 词： | 电子技术；有限差分法；逐次超松弛迭代法；最优松弛因子；静态场电势问题；求解线性方程组 |
| Title： | Research on finite difference method and successive over-relaxation iterative method for solving the potential of electrostatic field |
| Author： | SUN Hao, ZHU Xiaoying, WANG Shi |
| Organization： | School of Electronics and Information Engineering, Liaoning Technical University |
| Abstract： | Using the finite difference method to obtain the difference equations of static field, and using the successive over-relaxation iterative method to solve the difference equations of static field, then we can obtain the approximate solution of static field. In this paper, the solving problem of static field is taken as an example, Python is used to write programs and draw images, and then the correctness of this method is verified. At the same time, the influence of the number of iterations on the iterative error and the relationship between the optimal relaxation factor in the successive over-relaxation iterative method and the mesh density in the finite difference method are studied, which provides scientific reference for the application of the finite difference method and the successive over-relaxation iterative method in engineering problem. |
| Key words： | electronic technology; finite difference method; successive over-relaxation iterative method; optimal relaxation factor; static field potential problem; solve a system of linear equations |
| 发表期数： | 2020年12月第4期 |
| 引用格式： | 孙浩，朱笑莹，王诗. 对静电场电势求解的有限差分法和逐次超松弛迭代法的研究[J]. 中国科技论文在线精品论文，2020，13（4）：432-438. |
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