Shape Optimization of Supercapacitor Electrode to Maximize Charge Storage

TL;DR

This paper develops a mathematical framework for optimizing the shape of supercapacitor electrodes to enhance charge storage capacity, employing advanced PDE modeling, sensitivity analysis, and numerical algorithms in 2D and 3D.

Contribution

It introduces a novel shape optimization model for supercapacitor electrodes based on the coupled Poisson-Nernst-Planck system, with efficient numerical solution methods.

Findings

Optimized electrode shapes improve ionic concentration distribution.

Numerical algorithms effectively solve the shape optimization problem.

Results demonstrate potential for enhanced supercapacitor performance.

Abstract

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.