LLM Assisted Mathematical Modeling: Homogeneous Laplace Equation in Cylinder with the Complete Electrode Model

This paper presents an analytical solution for the potential distribution in Electrical Impedance Tomography (EIT) under the complete electrode model, extending previous work on a 2D homogeneous disk to a more realistic 3D cylindrical geometry of finite height. By taking into account for the influence of electrode height, this approach offers an improved representation compared to the earlier 2D formulation. The mathematical modeling involved in deriving this solution was significantly facilitated by the use of a Large Language Model (LLM), DeepSeek, which aided in the tedious index manipulations inherent in solving the Laplace equation with appropriate boundary conditions in cylindrical coordinates using methods of separation variables. This work is organized into three main, presenting the main result and Conlusion/future works followed by an Appendix detailing the step-by-step mathematical derivation assisted by LLM Deepseek.