A minimizing principle for the Poisson-Boltzmann equation

Abstract

The Poisson-Boltzmann equation is often presented via a variational formulation based on the electrostatic potential. However, the functional has the defect of being non-convex. It can not be used as a local minimization principle while coupled to other dynamic degrees of freedom. We formulate a convex dual functional which is numerically equivalent at its minimum and which is more suited to local optimization.

5 pages, 0 figures

References in corpus (3)

• Dipolar Poisson-Boltzmann Equation: Ions and Dipoles Close to Charged Surfaces
• Making Sense of the Legendre Transform
• Simple and Robust Solver for the Poisson-Boltzmann Equation

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• Continuum model of the simple dielectric fluid: Consistency between density based and continuum mechanics methods