Exact novel formulas and fast algorithm of potential for a hammock resistor network

The establishment of a resistor network model has become a sharp edge to solve complex scientific problems. In this paper, we introduce Chebyshev polynomials to express the potential formula of the hammock resistor network and improve the general solution of the hammock resistor network. Moreover, through the change in different parameters, special potential formulas are proposed and displayed in 3D dynamic view. A fast algorithm of the calculating potential is given by using the matrix equation model, discrete cosine transform-II, and the fast matrix-vector multiplication. Finally, we show the advantages of our improved potential formula and fast algorithm by the calculation efficiency of the three methods. The modified potential formula and the presented fast algorithm provide a new tool for the field of science and engineering.