We build a new mathematical model of shape optimization for maximizing ionic concentration governed by the multi-physical coupling steady-state Poisson-Nernst-Planck system. Shape sensitivity analysis is performed to obtain the Eulerian derivative of the cost functional. The Gummel fixed-point method with inverse harmonic averaging technique on exponential coefficient is used to solve efficiently the steady-state Poisson-Nernst-Planck system. Various numerical results using a shape gradient algorithm in 2d and 3d are presented.
@article{arxiv.2406.09616,
title = {Shape Optimization of Supercapacitor Electrode to Maximize Charge Storage},
author = {Jiajie Li and Shenggao Zhou and Shengfeng Zhu},
journal= {arXiv preprint arXiv:2406.09616},
year = {2025}
}