51 citations · 150 across the 19 of their papers we have counts for
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Local Structure-Preserving Relaxation Method for Charged Systems on Unstructured Meshes
Zhonghua Qiao, Zhenli Xu, Qian Yin +1
This work considers charged systems described by the modified Poisson--Nernst--Planck (PNP) equations, which incorporate ionic steric effects and the Born solvation energy for diel…
Second-order, Positive, and Unconditional Energy Dissipative Scheme for Modified Poisson-Nernst-Planck Equations
Jie Ding, Shenggao Zhou
First-order energy dissipative schemes in time are available in literature for the Poisson-Nernst-Planck (PNP) equations, but second-order ones are still in lack. This work propose…
Asymptotic analysis on charging dynamics for stack-electrode model of supercapacitors
Lijie Ji, Zhenli Xu, Shenggao Zhou
Supercapacitors are promising electrochemical energy storage devices due to their prominent performance in rapid charging/discharging rates, long cycle life, stability, etc. Experi…
A second order accurate numerical method for the Poisson-Nernst-Planck system in the energetic variational formulation
Chun Liu, Cheng Wang, Steven M. Wise +2
A second order accurate (in time) numerical scheme is proposed and analyzed for the Poisson-Nernst-Planck equation (PNP) system, reformulated as a non-constant mobility gr…
Structure-preserving numerical method for Maxwell-Ampère Nernst-Planck model
Zhonghua Qiao, Zhenli Xu, Qian Yin +1
Charge dynamics play essential role in many practical applications such as semiconductors, electrochemical devices and transmembrane ion channels. A Maxwell-Ampère Nernst-Planck (M…
Convergence Analysis of Structure-Preserving Numerical Methods Based on Slotboom Transformation for the Poisson--Nernst--Planck Equations
Jie Ding, Cheng Wang, Shenggao Zhou
The analysis of structure-preserving numerical methods for the Poisson--Nernst--Planck (PNP) system has attracted growing interests in recent years. In this work, we provide an opt…
Fast Newton Iterative Method for Local Steric Poisson--Boltzmann Theories in Biomolecular Solvation
Minhong Chen, Wei Dou, Shenggao Zhou
This work proposes a fast iterative method for local steric Poisson--Boltzmann (PB) theories, in which the electrostatic potential is governed by the Poisson's equation and ionic c…
A positivity-preserving, energy stable and convergent numerical scheme for the Poisson-Nernst-Planck system
Chun Liu, Cheng Wang, Steven M. Wise +2
In this paper we propose and analyze a finite difference numerical scheme for the Poisson-Nernst-Planck equation (PNP) system. To understand the energy structure of the PNP model,…
Structure-Preserving Numerical Methods for Nonlinear Fokker--Planck Equations with Nonlocal Interactions by an Energetic Variational Approach
Chenghua Duan, Wenbin Chen, Chun Liu +2
In this work, we develop novel structure-preserving numerical schemes for a class of nonlinear Fokker--Planck equations with nonlocal interactions. Such equations can cover many ca…
A Positive and Energy Stable Numerical Scheme for the Poisson-Nernst-Planck-Cahn-Hilliard Equations with Steric Interactions
Yiran Qian, Cheng Wang, Shenggao Zhou
We consider numerical methods for the Poisson-Nernst-Planck-Cahn-Hilliard (PNPCH) equations with steric interactions. We propose a novel energy stable numerical scheme that respect…
Structure-Preserving and Efficient Numerical Methods for Ion Transport
Jie Ding, Zhongming Wang, Shenggao Zhou
Ion transport, often described by the Poisson--Nernst--Planck (PNP) equations, is ubiquitous in electrochemical devices and many biological processes of significance. In this work,…
Computational Study on Hysteresis of Ion Channels: Multiple Solutions to Steady-State Poisson--Nernst--Planck Equations
Jie Ding, Hui Sun, Zhongming Wang +1
The steady-state Poisson-Nernst-Planck (ssPNP) equations are an effective model for the description of ionic transport in ion channels. It is observed that an ion channel exhibits…