A numerical energetic variational approach for constructing spectral schemes for PNP model


Chun-Hao Teng

13:20:00 - 14:10:00

101 , Mathematics Research Center Building (ori. New Math. Bldg.)

In this talk we will present a numerical procedure for constructing computa- tional schemes to simulate the dynamics of charge activities in ionic channel. Here we consider that the dynamics of charges is described by a PNP model satisfying an energy functional involving: (1) energy density functions of the ln ci with each ci representing a charge concentration, and (2) an form ci electrostatic potential represented by a convolution of a Green function and charge concentrations.

To illustrate the concepts in the present scheme construction procedure, we shall first based on a model wave problem, give a short discussion about the relationships between the energy estimate of the model problem and the numerical stability of a scheme for solving the wave equation. In the second part of the talk, we shall describe how to extend these concepts to construct a numerical scheme, based on pseudospectral penalty methods, for the PNP equations satisfying the aforementioned energy functional.