Efficient, positive, and energy stable schemes for multi-d Poisson-Nernst-Planck systems

DOI10.1007/s10915-021-01503-1zbMath1471.35277arXiv2001.08350OpenAlexW3159517390MaRDI QIDQ2031872

Wumaier Maimaitiyiming, Hai-liang Liu

Publication date: 15 June 2021

Published in: Journal of Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2001.08350

zbMATH Keywords

mass conservationpositivityenergy decayPoisson-Nernst-Planck equationssteady-statesemi-implicit discretization

Mathematics Subject Classification ID

PDEs in connection with biology, chemistry and other natural sciences (35Q92) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Statistical mechanics of semiconductors (82D37) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Finite difference methods for boundary value problems involving PDEs (65N06) General biology and biomathematics (92B05) Boundary value problems for second-order elliptic systems (35J57) Finite volume methods for boundary value problems involving PDEs (65N08)

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Cites Work

• Unnamed Item
• Unnamed Item
• A free energy satisfying finite difference method for Poisson-Nernst-Planck equations
• A mathematical model for the hard sphere repulsion in ionic solutions
• Second-order Poisson-Nernst-Planck solver for ion transport
• On the Chang and Cooper scheme applied to a linear Fokker-Planck equation
• Energetically stable discretizations for charge transport and electrokinetic models
• A modified Poisson-Nernst-Planck model with excluded volume effect: theory and numerical implementation
• A free energy satisfying discontinuous Galerkin method for one-dimensional Poisson-Nernst-Planck systems
• An energy preserving finite difference scheme for the Poisson-Nernst-Planck system
• Poisson-Nernst-Planck systems for ion flow with density functional theory for hard-sphere potential: I-V relations and critical potentials. I: Analysis
• Positive and free energy satisfying schemes for diffusion with interaction potentials
• A fully discrete positivity-preserving and energy-dissipative finite difference scheme for Poisson-Nernst-Planck equations
• A conservative, free energy dissipating, and positivity preserving finite difference scheme for multi-dimensional nonlocal Fokker-Planck equation
• Positivity preserving finite difference methods for Poisson-Nernst-Planck equations with steric interactions: application to slit-shaped nanopore conductance
• A positivity preserving and free energy dissipative difference scheme for the Poisson-Nernst-Planck system
• Analysis and practical use of flexible biCGStab
• Linearized conservative finite element methods for the Nernst-Planck-Poisson equations
• Poisson-Nernst-Planck equations for simulating biomolecular diffusion-reaction processes. I: Finite element solutions
• Nonlinear Poisson–Nernst–Planck equations for ion flux through confined geometries
• An Entropy Satisfying Conservative Method for the Fokker–Planck Equation of the Finitely Extensible Nonlinear Elastic Dumbbell Model
• Continuum electrostatics for ionic solutions with non-uniform ionic sizes
• Consistency of Semiconductor Modeling: An Existence/Stability Analysis for the Stationary Van Roosbroeck System
• Qualitative Properties of Steady-State Poisson--Nernst--Planck Systems: Mathematical Study
• 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
• Variational Multiscale Models for Charge Transport
• Error Estimates for the Iterative Discontinuous Galerkin Method to the Nonlinear Poisson-Boltzmann Equation
• Unconditional Positivity-Preserving and Energy StableSchemesforaReducedPoisson-Nernst-Planck System
• A Flexible Inner-Outer Preconditioned GMRES Algorithm
• Geometric Singular Perturbation Approach to Steady-State Poisson--Nernst--Planck Systems
• An Iterative Discontinuous Galerkin Method for Solving the Nonlinear Poisson Boltzmann Equation
• Numerical Solution of 3D Poisson-Nernst-Planck Equations Coupled with Classical Density Functional Theory for Modeling Ion and Electron Transport in a Confined Environment