Solution of Partial Differential Equations with a Resistance Network Analogue
Solution of Partial Differential Equations with a Resistance Network Analogue
复制标题
用电阻网络模拟解偏微分方程
DOI：
10.1088/0508-3443/1/4/303
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发表时间：
1950
期刊：
影响因子：
--
通讯作者：
G. Liebmann
中科院分区：
文献类型：
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作者：
G. Liebmann
本文表明，由于电阻网络具有一定的平均特性，因此在给定边界条件下，电阻网络能够以非常高的精度求解偏微分方程。对作者构建的电阻网络进行了相当详尽的测试，其精度在千分之一到万分之一之间。描述了该电阻网络的设计；为轴对称型，z向60目，r向20目，周围有终端条。提供五十个电流馈入点用于调节边界条件。模型的边界不需要与网格点重合，因为可以通过网络的局部修改来进行校正。还可以在网络网格内进行测量并模拟将介电材料引入电场。高精度、操作简单和速度快，使得电阻网络成为科学和工程许多分支研究场分布的有用工具。
It is shown in this paper that resistance networks are capable of very high accuracy in the solution of partial differential equations with given boundary conditions, as the networks possess certain averaging properties. Fairly exhaustive tests carried out on a resistance network constructed by the author gave accuracies in the range of 1 part in 1 000 to 1 part in 10 000. The design of this resistance network is described; it is of the axially symmetrical type, with 60 meshes in the z-direction and 20 meshes in the r-direction, and is surrounded by a termination strip. Fifty current feeding points for adjusting boundary conditions are provided. The boundaries of the models need not coincide with the mesh points as correction can be made by local modifications of the network. It is also possible to take measurements within a mesh of the network and to simulate the introduction of dielectric material into an electric field. The high accuracy, and simplicity and speed of operation, make the resistance network a useful tool in the investigation of field distributions in many branches of science and engineering.