Volume 14, Issue 4-5
New Finite Element Iterative Methods for Solving a Nonuniform Ionic Size Modified Poisson-Boltzmann Equation.

Dexuan Xie

Int. J. Numer. Anal. Mod., 14 (2017), pp. 688-711

Published online: 2017-08

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  • 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.

  • Keywords

Poisson-Boltzmann equation finite element method nonlinear successive overrelaxation ionic size effects electrostatics

  • AMS Subject Headings

92-08 65N30 92C40

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COPYRIGHT: © Global Science Press

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@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 = {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.}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/10056.html} }
TY - JOUR T1 - New Finite Element Iterative Methods for Solving a Nonuniform Ionic Size Modified Poisson-Boltzmann Equation. AU - Dexuan Xie 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 KW - finite element method KW - nonlinear successive overrelaxation KW - ionic size effects KW - electrostatics AB - 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.
Dexuan Xie. (1970). New Finite Element Iterative Methods for Solving a Nonuniform Ionic Size Modified Poisson-Boltzmann Equation.. International Journal of Numerical Analysis and Modeling. 14 (4-5). 688-711. doi:
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