对静电场电势求解的有限差分法和超松弛迭代法的研究
首发时间:2020-06-05
摘要:有限差分法是静态场电位问题数值解的有效方法。通过有限差分法求得静态场的差分方程组,然后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,研究了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以及超松弛迭代法中迭代次数对误差的影响,为有限差分法和超松弛迭代法在工程问题中的应用提供科学参考。
关键词: 有限差分法 超松弛迭代法 最优松弛因子 静态场电位问题 Python 求解线性方程组
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The research of the finite difference method and the successive Over-relaxation iterative method for solving the potential of electrostatic field
Abstract:The finite difference method is an effective method for the numerical solution of static field potential problems.Use the finite difference method to obtain the difference equations of static field, and then use the successive Overrelaxation iterative method to solve the difference equations of static field, the approximate solution of static field can be obtained. This paper take the problem of solving static field as an example, use Python to write programs and draw images, the relationship between the optimal relaxation factor and the mesh density in the finite difference method and the influence of the number of iterations on the errors in the method are studied, which provides a scientificreference for the application of the finite difference method and the overrelaxation iterative method in engineering problems.
Keywords: Finite difference method Overrelaxation iterative method Optimal relaxation factor Static field potential problem Python Solve a system of linear equations
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对静电场电势求解的有限差分法和超松弛迭代法的研究
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