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, the speaker is 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 roundoff error) a discretized form of the energy dynamics of the system as well as preserve positivity. Also Kabre would like to study the effect of the conservation on long-term behavior of the simulation, and include distributions of permanent charges for investigating selectivity of ion channels.

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Graduate Student

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