@Article{IJNAM-14-688,
author = {Dexuan Xie},
title = {New Finite Element Iterative Methods for Solving a Nonuniform Ionic Size Modified Poisson-Boltzmann Equation},
journal = {International Journal of Numerical Analysis and Modeling},
year = {2017},
volume = {14},
number = {4-5},
pages = {688--711},
abstract = {<p style="text-align: justify;">In this paper, a nonuniform size modified Poisson-Boltzmann equation (SMPBE)
for a protein in a solvent with multiple ionic species in distinct ionic sizes is derived by using a
new electrostatic free energy functional and solution decomposition techniques. It is then proved
to have a unique solution, and the solution satisfies a system consisting of nonlinear algebraic
equations and one Poisson dielectric interface problem. To solve it numerically, two new finite
element iterative schemes are proposed by using nonlinear successive over-relaxation techniques,
along with an improved uniform SMPBE for generating initial iterates. Furthermore, they are
programmed in Python and Fortran as a software package for solving the nonuniform SMPBE,
and numerically tested on a Born ball test model and a protein in a sodium chloride solution and
a sodium chloride and potassium chloride solution. Numerical results confirm the convergence of
the two new iterative schemes and demonstrate the high performance of the new software package.</p>},
issn = {2617-8710},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/ijnam/10056.html}
}