报告题目：Structure-preserving numerical method for Maxwell-Ampère Nernst-Planck model

报告人：乔中华教授香港理工大学

报告时间：2023年11月15日15:00-16:00

报告地点：数学院235

报告摘要：Charge dynamics play essential role in many practical applications such as semiconductors, electrochemical devices and transmembrane ion channels. A Maxwell-Ampère Nernst-Planck (MANP) model that describes charge dynamics via concentrations and the electric displacement is able to take effects beyond mean-field approximations into account. To obtain physically faithful numerical solutions, we develop a structure-preserving numerical method for the MANP model whose solution has several physical properties of importance. By the Slotboom transform with entropic-mean approximations, a positivity preserving scheme with Scharfetter-Gummel fluxes is derived for the generalized Nernst-Planck equations. To deal with the curl-free constraint, the dielectric displacement from the Maxwell-Ampère equation is further updated with a local relaxation algorithm of linear computational complexity. We prove that the proposed numerical method unconditionally preserves the mass conservation and the solution positivity at the discrete level and satisfies the discrete energy dissipation law with a time-step restriction. Numerical experiments verify that our numerical method has expected accuracy and structure-preserving properties. Applications to ion transport with large convection, arising from boundary-layer electric field and Born solvation interactions, further demonstrate that the MANP formulation with the proposed numerical scheme has attractive performance and can effectively describe charge dynamics with large convection of high numerical cell Péclet numbers.

乔中华，2006年在香港浸会大学获得博士学位，现为香港理工大学应用数学系教授。乔中华教授主要从事数值微分方程方面算法设计及分析，近年来研究工作集中在相场方程的数值模拟及计算流体力学的高效算法。他至今在SCI期刊上发表论文70余篇，部分成果发表在Math. Comp.,SIAM J. Appl. Math., SIAM J. Numer. Anal., SIAM J. Sci. Comput., J. Comput. Phys.,IMA J. Numer. Anal.等计算、应用数学领域著名期刊，文章被合计引用2000余次。他于2013年获香港研究资助局颁发2013至2014年度杰出青年学者奖，于2018年获得香港数学会青年学者奖，并且于2020年获得香港研究资助局研究学者奖。