Energy-Conserving Numerical Scheme for the Poisson-Nerst-Plank Equations

The Poisson-Nernst-Planck equations are a system of nonlinear partial differential equations that describe flow of charged particles in solution. In particular, we are interested in the transport of ions in the biological membrane proteins (ion channels). This work is about the design of numerical schemes that preserve exactly (up to round-off error) a discretized form of the energy dynamics of the system. We will present a scheme that achieves the goal of preserving the energy dissipation law and some preliminary numerical results.

Event Topic

Stochastic & Multiscale Modeling and Computation