Computationally Efficient Technique for Nonlinear Poisson-Boltzmann Equation

TL;DR

This paper introduces an adaptive tolerance method for solving nonlinear Poisson-Boltzmann equations more efficiently, reducing computational effort while maintaining accuracy, and easily integrating into existing simulation tools.

Contribution

The paper presents a novel adaptive tolerance approach for Jacobian systems in Newton's method applied to nonlinear Poisson-Boltzmann equations, improving computational efficiency.

Findings

Significant reduction in computational work compared to traditional methods

The algorithm maintains accuracy while saving resources

Easy integration into existing simulation frameworks

Abstract

Discretization of non-linear Poisson-Boltzmann Equation equations results in a system of non-linear equations with symmetric Jacobian. The Newton algorithm is the most useful tool for solving non-linear equations. It consists of solving a series of linear system of equations (Jacobian system). In this article, we adaptively define the tolerance of the Jacobian systems. Numerical experiment shows that compared to the traditional method our approach can save a substantial amount of computational work. The presented algorithm can be easily incorporated in existing simulators.