TY - JOUR
T1 - New Finite Element Iterative Methods for Solving a Nonuniform Ionic Size Modified Poisson-Boltzmann Equation
JO - International Journal of Numerical Analysis and Modeling
VL - 4-5
SP - 688
EP - 711
PY - 2017
DA - 2017/08
SN - 14
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/10056.html
KW - Poisson-Boltzmann equation, finite element method, nonlinear successive over-relaxation, ionic size effects, electrostatics.
AB - <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>