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Fast algorithm and new potential formula represented by Chebyshev polynomials for an [Formula: see text] globe

Yufan Zhou1, Yanpeng Zheng2, Xiaoyu Jiang1

  • 1School of Information Science and Engineering, Linyi University, Linyi, 276000 China.

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|December 8, 2022
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This study introduces a new potential formula for resistor networks using Chebyshev polynomials and a fast algorithm. This method significantly speeds up calculations for large-scale resistor network analysis.

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Area of Science:

  • Electrical Engineering
  • Computational Physics
  • Applied Mathematics

Background:

  • Resistor networks are fundamental in electronics.
  • Manual calculation limits the scale of resistor network analysis.
  • Numerical simulation is trending for large-scale operations.

Purpose of the Study:

  • To improve the general solution of potential formulas for globe resistor networks.
  • To introduce Chebyshev polynomials for a new potential formula.
  • To develop an efficient algorithm for machine calculation of potential.

Main Methods:

  • Utilizing Chebyshev polynomials to derive a new potential formula for globe networks.
  • Proposing a discrete cosine transform type II (DCT-II) algorithm for potential computation.
  • Applying the new formula to derive equivalent resistance in special cases.

Main Results:

  • The new potential formula using Chebyshev polynomials offers significant time savings.
  • The proposed DCT-II algorithm greatly increases the efficiency of potential computation.
  • Equivalent resistance formulas for special cases were derived and visualized.

Conclusions:

  • The developed potential formula and fast algorithm enable large-scale resistor network operations.
  • This approach enhances computational efficiency for complex resistor network problems.
  • The findings facilitate advanced analysis and design of resistor networks.