Simple and Robust Solver for the Poisson-Boltzmann Equation

Details Simple and Robust Solver for the Poisson-Boltzmann Equation Simple and Robust Solver for the Poisson-Boltzmann Equation

2008-10-02

arxiv.org/abs/0810.0490v3

Physics

Condensed Matter

Soft Condensed Matter

11 pages, 5 figures, 2 tables

Scientific paper

A variational approach is used to develop a robust numerical procedure for solving the nonlinear Poisson-Boltzmann equation. Following Maggs et al., we construct an appropriate constrained free energy functional, such that its Euler-Lagrange equations are equivalent to the Poisson-Boltzmann equation. We then develop, implement, and test an algorithm for its numerical minimization, which is quite simple and unconditionally stable. The analytic solution for planar geometry is used for validation. Furthermore, some results are presented for a charged colloidal sphere surrounded by counterions.

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