New Finite Element Iterative Methods for Solving a Nonuniform Ionic Size Modified Poisson-Boltzmann Equation
Year: 2017
International Journal of Numerical Analysis and Modeling, Vol. 14 (2017), Iss. 4-5 : pp. 688–711
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2017-IJNAM-10056
International Journal of Numerical Analysis and Modeling, Vol. 14 (2017), Iss. 4-5 : pp. 688–711
Published online: 2017-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 24
Keywords: Poisson-Boltzmann equation finite element method nonlinear successive over-relaxation ionic size effects electrostatics.