An iterative method for finite-element solutions of the nonlinear Poisson-Boltzmann equation

Authors:
Ren-Chuen Chen
Affiliations:
National Kaohsiung Normal University, Department of Mathematics, Kaohsiung City, Taiwan (R.O.C.)
Venue:
WSEAS Transactions on Computers
Year:
2008

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Abstract

A finite-element (FE) approach combined with an efficient iterative method have been used to provide a numerical solution of the nonlinear Poisson-Boltzmann equation. The iterative method solves the nonlinear equations arising from the FE discretization procedure by a node-by-node calculation. Moreover, some extensions called by Picard, Gauss-Seidel, and successive overrelaxation (SOR) methods are also presented and analyzed for the FE solution. The performances of the proposed methods are illustrated by applying them to the problem of two identical colloidal particles in a symmetric electrolyte. My numerical results are found in good agreement with the previous published results. A comprehensive survey is also given for the accuracy and efficiency of these methods.