A novel algebraic topological method-based approach for evaluating stored electrostatic energy and 3D Maxwellian capacitance

Abstract

This paper presents a new and first of its kind approach for numerical evaluation of stored electrostatic energy and capacitance using Algebraic Topological Method (ATM). The ATM is an alternative computing technique with certain advantages over conventional methods such as Finite Difference Method, Finite Element Method, and Method of Moments because it can formulate Multiphysics problems using direct discrete forms instead of partial differential equations. As a proof of concept, the approach has been validated in ideal 1D, 2D and 3D capacitors and the relative error was found to be <1 % when compared with corresponding analytical solutions. Further the problems of capacitors with simple 3D geometries were solved and the relative error found to be <3 % using refined mesh. The numerical stability of the proposed approach for different mesh sizes is investigated and the effect of modeling space is also studied in detail. Finally, the applicability of ATM is benchmarked with the Finite Element Method and experimental results in the case of real capacitors used in engineering applications. The results show that the proposed approach holds great potential for advancing the field of capacitor devices design and optimization by means of modeling and virtual prototyping.