Mathematics Faculty Articles

Title

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.

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.

Additional Comments

Copyright © 2017, Springer Science Business Media New York

ORCID ID

0000-0001-7817-4308

DOI

10.1007/s10825-017-0969-8

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