Mathematics Faculty Articles
An energy-preserving discretization for the Poisson–Nernst–Planck equations
Document Type
Article
Publication Date
3-6-2017
Publication Title
Journal of Computational Electronics
Keywords
Poisson–Nernst–Planck equations, Energy conservation, Finite difference, Ion channels
ISSN
1569-8025
Volume
16
First Page
431
Last Page
441
Abstract
The Poisson–Nernst–Planck (PNP) equations have recently been used to describe the dynamics of ion transport through biological ion channels besides being widely employed in semiconductor industry. This paper is about the design of a numerical scheme to solve the PNP equations that preserves exactly (up to roundoff error) a discretized form of the energy dynamics of the system. The proposed finite difference scheme is of second-order accurate in both space and time. Comparisons are made between this energy dynamics-preserving scheme and a standard finite difference scheme, showing a difference in satisfying the energy law. Numerical results are presented for validating the orders of convergence in both time and space of the new scheme for the PNP system.
Additional Comments
Copyright © 2017, Springer Science Business Media New York
NSUWorks Citation
Flavell, Allen; Kabre, Julienne; and Li, Xiaofan, "An energy-preserving discretization for the Poisson–Nernst–Planck equations" (2017). Mathematics Faculty Articles. 320.
https://nsuworks.nova.edu/math_facarticles/320
ORCID ID
0000-0001-7817-4308
DOI
10.1007/s10825-017-0969-8
Comments
The work is partially supported by NSF under the grant DMS-1620449. The authors would like to thank Bob Eisenberg and Chun Liu for helpful discussion on the research.