Speaker: Wang zhong ming(Associate professor,  Florida International University)

Title: Finite difference methods for the multi-dimensional Poisson--Nernst--Planck equations

Abstract: We design and analyze some finite difference methods for solving the Poisson-Nernst-Planck (PNP) equations. Central-differencing discretization based finite difference methods are proposed for the Nernst--Planck (NP) with geometric-mean/harmonic-mean types of approximations. The numerical schemes, with proper time discretization, respect three desired properties that are possessed by analytical solutions: I) conservation, II) positivity of solution, and III) free-energy dissipation. The semi-implicit scheme based on the harmonic-mean approximation is further shown to preserve positivity unconditionally and have bounded condition numbers of the associated matrix.  Numerical experiments validate the numerical analysis. An application to an electrochemical charging system is also studied to demonstrate the effectiveness of our schemes in solving realistic problems. This is a joint work with, J. Ding, H. Liu and S. Zhou.

Time: 10:00Am, 24/07/2019

Location: room702, Science and technology building(south)