Efficient, Positive, and Energy Stable Schemes for Multi-D Poisson–Nernst–Planck Systems

A fully discrete positivity-preserving and energy-dissipative finite difference scheme for Poisson–Nernst–Planck equations

(2020) Jingwei Hu et al.   NUMERISCHE MATHEMATIK

Positive and free energy satisfying schemes for diffusion with interaction potentials

(2020) Hailiang Liu et al.   JOURNAL OF COMPUTATIONAL PHYSICS

A conservative, free energy dissipating, and positivity preserving finite difference scheme for multi-dimensional nonlocal Fokker–Planck equation

(2019) Yiran Qian et al.   JOURNAL OF COMPUTATIONAL PHYSICS

A Positivity Preserving and Free Energy Dissipative Difference Scheme for the Poisson–Nernst–Planck System

(2019) Dongdong He et al.   JOURNAL OF SCIENTIFIC COMPUTING

Positivity preserving finite difference methods for Poisson–Nernst–Planck equations with steric interactions: Application to slit-shaped nanopore conductance

(2019) Jie Ding et al.   JOURNAL OF COMPUTATIONAL PHYSICS

A modified Poisson–Nernst–Planck model with excluded volume effect: theory and numerical implementation

(2018) Farjana Siddiqua et al.   Communications in Mathematical Sciences

Analysis of the Mean Field Free Energy Functional of Electrolyte Solution with Nonhomogenous Boundary Conditions and the Generalized PB/PNP Equations with Inhomogeneous Dielectric Permittivity

(2018) Xuejiao Liu et al.   SIAM JOURNAL ON APPLIED MATHEMATICS

A free energy satisfying discontinuous Galerkin method for one-dimensional Poisson–Nernst–Planck systems

(2017) Hailiang Liu et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Linearized Conservative Finite Element Methods for the Nernst–Planck–Poisson Equations

(2017) Huadong Gao et al.   JOURNAL OF SCIENTIFIC COMPUTING

Cross Interaction Drives Stratification in Drying Film of Binary Colloidal Mixtures

(2017) Jiajia Zhou et al.   PHYSICAL REVIEW LETTERS

An energy-preserving discretization for the Poisson–Nernst–Planck equations

(2017) Allen Flavell et al.   Journal of Computational Electronics

Energetically stable discretizations for charge transport and electrokinetic models

(2016) Maximilian S. Metti et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Analysis and Practical Use of Flexible BiCGStab

(2016) Jie Chen et al.   JOURNAL OF SCIENTIFIC COMPUTING

An Iterative Discontinuous Galerkin Method for Solving the Nonlinear Poisson Boltzmann Equation

(2016) Peimeng Yin et al.   Communications in Computational Physics

Numerical Solution of 3D Poisson-Nernst-Planck Equations Coupled with Classical Density Functional Theory for Modeling Ion and Electron Transport in a Confined Environment

(2016) Da Meng et al.   Communications in Computational Physics

A free energy satisfying finite difference method for Poisson–Nernst–Planck equations

(2014) Hailiang Liu et al.   JOURNAL OF COMPUTATIONAL PHYSICS

On the Chang and Cooper scheme applied to a linear Fokker-Planck equation

(2013) Christophe Buet et al.   Communications in Mathematical Sciences

A mathematical model for the hard sphere repulsion in ionic solutions

(2013) Bob Eisenberg et al.   Communications in Mathematical Sciences

Poisson–Nernst–Planck Systems for Ion Flow with Density Functional Theory for Hard-Sphere Potential: I–V Relations and Critical Potentials. Part I: Analysis

(2012) Shuguan Ji et al.   Journal of Dynamics and Differential Equations

Nonlinear Poisson–Nernst–Planck equations for ion flux through confined geometries

(2012) M Burger et al.   NONLINEARITY

An Entropy Satisfying Conservative Method for the Fokker–Planck Equation of the Finitely Extensible Nonlinear Elastic Dumbbell Model

(2012) Hailiang Liu et al.   SIAM JOURNAL ON NUMERICAL ANALYSIS

Variational Multiscale Models for Charge Transport

(2012) Guo-Wei Wei et al.   SIAM REVIEW

Poisson–Boltzmann–Nernst–Planck model

(2011) Qiong Zheng et al.   JOURNAL OF CHEMICAL PHYSICS

Second-order Poisson–Nernst–Planck solver for ion transport

(2011) Qiong Zheng et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Multiscale Simulations of Li Ion Conductivity in Solid Electrolyte

(2011) Maria L. Sushko et al.   Journal of Physical Chemistry Letters

Poisson–Nernst–Planck equations for simulating biomolecular diffusion–reaction processes I: Finite element solutions

(2010) Benzhuo Lu et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Continuum electrostatics for ionic solutions with non-uniform ionic sizes

(2009) Bo Li   NONLINEARITY