8 citations · 12 across the 4 of their papers we have counts for
8 papers
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…
The Calculus of Boundary Variations and the Dielectric Boundary Force in the Poisson-Boltzmann Theory for Molecular Solvation
Bo Li, Zhengfang Zhang, Shenggao Zhou
In a continuum model of the solvation of charged molecules in an aqueous solvent, the classical Poisson-Boltzmann (PB) theory is generalized to include the solute point charges and…
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,…
Hysteresis and Linear Stability Analysis on Multiple Steady-State Solutions to the Poisson--Nernst--Planck equations with Steric Interactions
Jie Ding, Hui Sun, Shenggao Zhou
In this work, we numerically study linear stability of multiple steady-state solutions to a type of steric Poisson--Nernst--Planck (PNP) equations with Dirichlet boundary condition…
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…