An inverse averaging finite element method for solving three-dimensional Poisson-Nernst-Planck equations in nanopore...

Area of Science:

• Computational physics and chemistry
• Nanotechnology and materials science
• Numerical analysis

Background:

• The Poisson-Nernst-Planck (PNP) model is crucial for simulating ion transport in nanopore systems.
• Standard numerical methods face convergence and stability issues with large nanopore systems and convection-dominated Nernst-Planck (NP) equations.

Purpose of the Study:

• To develop a robust and accurate numerical method for solving the 3D PNP model in nanopore simulations.
• To address the convergence difficulties and numerical instability associated with convection-dominated NP equations.

Main Methods:

• Introduced Slotboom variables to transform NP equations into self-adjoint second-order elliptic equations.
• Applied an inverse averaging technique to approximate exponential coefficients using harmonic averages on tetrahedral elements.
• Developed the inverse averaging finite element method (IAFEM) for solving the 3D PNP model.

Main Results:

• The IAFEM demonstrates good convergence for single and porous nanopore systems.
• The method remains stable even for convection-dominated NP equations.
• IAFEM ensures conservation of computed currents, a key advantage over other schemes.
• Numerical experiments confirm the accuracy and robustness of IAFEM, outperforming standard FEM for convection-dominated problems.

Conclusions:

• The proposed IAFEM is an effective and robust numerical technique for simulating 3D nanopore systems, including interconnected structures.
• IAFEM successfully overcomes the limitations of traditional methods in handling convection-dominated transport phenomena.
• The method's ability to maintain current conservation makes it highly valuable for accurate nanopore simulations.