Research articles
ScienceAsia 50 (2024):ID 2024100 1-10 |doi:
10.2306/scienceasia1513-1874.2024.100
New analytical function of potential and fast algorithm for
solving potentials in m x n fan resistor network
Gaojun Zhanga, Xiaoyu Jianga,*, Yanpeng Zhengb,*, Zhaolin Jiangc
ABSTRACT: This paper presents a refined analytical potential function (APF) for the m?n fan resistor network. Firstly,
the original piecewise APFs are replaced with a single analytic function, which improves the calculation scalability.
Secondly, Chebyshev polynomials of the second class are introduced to represent the analytical function of potential. A
fast algorithm for calculating potentials is then developed using the sixth type of discrete sine transform, significantly
reducing the computation time required for potential calculations. The paper simultaneously solves the APFs for several
special cases, presenting their potentials in three-dimensional views. Finally, experiments are conducted to analyze the
time and scalability of different methods for calculating the potential. The results of these experiments demonstrate
that the improved potential function and fast algorithm enable efficient manipulation of large-scale resistor networks,
the application scale of the original APF has been expanded.
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| a |
School of Information Science and Engineering, Linyi University, Linyi 276000 China |
| b |
School of Automation and Electrical Engineering Linyi University, Linyi 276000 China |
| c |
School of Mathematics and Statistics, Linyi University, Linyi 276000 China |
* Corresponding author, E-mail: jxy19890422@sina.com, zhengyanpeng0702@sina.com
Received 18 Jul 2023, Accepted 26 Sep 2024
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