Shape optimization for maximizing ionic concentration constrained by steady-state Poisson-Nernst-Planck system

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 metho...

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Bibliographic Details
Published inarXiv.org
Main Authors Li, Jiajie, Zhou, Shenggao, Zhu, Shengfeng
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 13.06.2024
Subjects
Algorithms
Cost analysis
Maximization
Sensitivity analysis
Shape optimization
Steady state
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Summary: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.
ISSN:2331-8422