报告人：江兆林（临沂大学）

时 间：2024年3月20日16:30

地 点：海韵园数理大楼686会议室

内容摘要:

Resistor network is widely used. Many potential formulae of resistor networks have been solved accurately, but the scale of data is limited by manual calculation, and numerical simulation has become the trend of large-scale operation. In this talk, a horn torus resistor network with an arbitrary boundary is researched. According to the modified Recursion-Transform method (RT-V), we obtain the general solution potential formula between two points on any axis. Firstly, the recursive matrix equation model is established by a perturbed tridiagonal Toeplitz matrix, and then the orthogonal matrix transformation is constructed to obtain the eigenvalues and eigenvectors of this perturbed tridiagonal Toeplitz matrix; Secondly, the boundary condition constraint equation model is established; Finally, the solution of the node voltage is given by using the inverse matrix transformation. We introduce Chebyshev polynomials to represent the general solution of the resistor network. In addition, a fast algorithm for solving matrix equations is proposed by using the famous fifth type of discrete sine transform. In the application of the formula, the equivalent resistance formulae in special cases are given and displayed by a three-dimensional dynamic view. The potential formula and the proposed fast algorithm realize large-scale operation.

个人简介：

江兆林，临沂大学校特聘二级教授、博士生导师。主要从事图象处理、复杂网络、神经网络、机器人路径规划、计算机数学的理论、算法及其应用、数值线代数等方面的研究工作。已在Physical Review E、Expert Systems with Applications等国内外期刊发表学术论文160余篇，出版专著1部，先后主持或参与国家级、省级课题等19项。

联系人：白正简