Solving Fluctuation-Enhanced Poisson-Boltzmann Equations

Abstract

Electrostatic correlations and fluctuations in ionic systems can be described within an extended Poisson-Boltzmann theory using a Gaussian variational form. The resulting equations are challenging to solve because they require the solution of a non-linear partial differential equation for the pair correlation function. This has limited existing studies to simple approximations or to one-dimensional geometries. In this paper we show that the numerical solution of the equations is greatly simplified by the use of selective inversion of a finite difference operator which occurs in the theory. This selective inversion preserves the sparse structure of the problem and leads to substantial savings in computer effort. In one and two dimensions further simplifications are made by using a mixture of selective inversion and Fourier techniques.

10 pages

References in corpus (4)

• Statics and Dynamics of Strongly Charged Soft Matter
• Perspective: Coulomb fluids -- weak coupling, strong coupling, in between and beyond
• Electrostatic correlations in inhomogeneous charged fluids beyond loop expansion
• Fluctuation-induced interactions between dielectrics in general geometries

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