## Efficient, positive, and energy stable schemes for Poisson-Nernst-Planck systems

- Feb. 21, 2020
- 2:30 p.m.
- LeConte 317R

## Abstract

We are concerned with positive and energy-dissipating schemes for solving the time-dependent system of Poisson-Nernst-Planck (PNP) equations, which has found much use in the modeling of biological membrane channels and semiconductor devices. As a gradient flow in density space, this strongly coupled system of nonlinear equations can take long time evolution to reach steady states. Hence, designing efficient and stable methods is highly desirable. In this talk we shall present a class of methods with structure-preserving properties for the PNP system, and review advances around related models such as the quantum diffusion equation.