Adaptive finite-element

Solution of the nonlinear Poisson-Boltzmann equation: A charged spherical particle at various distances from a charged cylindrical pore in a charged planar surface

W. Richard Bowen, Adel O. Sharif

Research output: Contribution to journalArticle

41 Citations (Scopus)

Abstract

A Galekin finite-element approach combined with an error estimator and automatic mesh refinement has been used to provide a flexible numerical solution of the Poisson-Boltzmann equation. A Newton sequence technique was used to solve the nonlinear equations arising from the finite-element discretization procedure. Errors arising from the finite-element solution due to mesh refinement were calculated using the Zienkiewicz-Zhu error estimator, and an automatic remeshing strategy was adopted to achieve a solution satisfying a preset quality. Examples of the performance of the error estimator in adaptive mesh refinement are presented. The adaptive finite-element scheme presented in this study has proved to he an effective technique in minimizing errors in finite-element solutions for a given problem, in particular those of complex geometries. As an example, numerical solutions are presented for the case of a charged spherical particle at various distances from a charged cylindrical pore in a charged planar surface. Such a scheme provides a quantification of the significance of electrostatic interactions for an important industrial technology-membrane separation processes.

Original languageEnglish
Pages (from-to)363-374
Number of pages12
JournalJournal of Colloid and Interface Science
Volume187
Issue number2
DOIs
Publication statusPublished - 15 Mar 1997
Externally publishedYes

Fingerprint

Boltzmann equation
porosity
estimators
Membrane technology
Coulomb interactions
Nonlinear equations
newton
nonlinear equations
electrostatics
membranes
Geometry
geometry
interactions

Keywords

  • Adaptivity
  • Boltzman equation
  • Finite element
  • Membrane
  • Poisson
  • Sphere-pore interaction

ASJC Scopus subject areas

  • Colloid and Surface Chemistry
  • Physical and Theoretical Chemistry
  • Surfaces and Interfaces

Cite this

@article{1785ab0f0bec4c399749fd81545a1ace,
title = "Adaptive finite-element: Solution of the nonlinear Poisson-Boltzmann equation: A charged spherical particle at various distances from a charged cylindrical pore in a charged planar surface",
abstract = "A Galekin finite-element approach combined with an error estimator and automatic mesh refinement has been used to provide a flexible numerical solution of the Poisson-Boltzmann equation. A Newton sequence technique was used to solve the nonlinear equations arising from the finite-element discretization procedure. Errors arising from the finite-element solution due to mesh refinement were calculated using the Zienkiewicz-Zhu error estimator, and an automatic remeshing strategy was adopted to achieve a solution satisfying a preset quality. Examples of the performance of the error estimator in adaptive mesh refinement are presented. The adaptive finite-element scheme presented in this study has proved to he an effective technique in minimizing errors in finite-element solutions for a given problem, in particular those of complex geometries. As an example, numerical solutions are presented for the case of a charged spherical particle at various distances from a charged cylindrical pore in a charged planar surface. Such a scheme provides a quantification of the significance of electrostatic interactions for an important industrial technology-membrane separation processes.",
keywords = "Adaptivity, Boltzman equation, Finite element, Membrane, Poisson, Sphere-pore interaction",
author = "Bowen, {W. Richard} and Sharif, {Adel O.}",
year = "1997",
month = "3",
day = "15",
doi = "10.1006/jcis.1996.4705",
language = "English",
volume = "187",
pages = "363--374",
journal = "Journal of Colloid and Interface Science",
issn = "0021-9797",
publisher = "Academic Press Inc.",
number = "2",

}

TY - JOUR

T1 - Adaptive finite-element

T2 - Solution of the nonlinear Poisson-Boltzmann equation: A charged spherical particle at various distances from a charged cylindrical pore in a charged planar surface

AU - Bowen, W. Richard

AU - Sharif, Adel O.

PY - 1997/3/15

Y1 - 1997/3/15

N2 - A Galekin finite-element approach combined with an error estimator and automatic mesh refinement has been used to provide a flexible numerical solution of the Poisson-Boltzmann equation. A Newton sequence technique was used to solve the nonlinear equations arising from the finite-element discretization procedure. Errors arising from the finite-element solution due to mesh refinement were calculated using the Zienkiewicz-Zhu error estimator, and an automatic remeshing strategy was adopted to achieve a solution satisfying a preset quality. Examples of the performance of the error estimator in adaptive mesh refinement are presented. The adaptive finite-element scheme presented in this study has proved to he an effective technique in minimizing errors in finite-element solutions for a given problem, in particular those of complex geometries. As an example, numerical solutions are presented for the case of a charged spherical particle at various distances from a charged cylindrical pore in a charged planar surface. Such a scheme provides a quantification of the significance of electrostatic interactions for an important industrial technology-membrane separation processes.

AB - A Galekin finite-element approach combined with an error estimator and automatic mesh refinement has been used to provide a flexible numerical solution of the Poisson-Boltzmann equation. A Newton sequence technique was used to solve the nonlinear equations arising from the finite-element discretization procedure. Errors arising from the finite-element solution due to mesh refinement were calculated using the Zienkiewicz-Zhu error estimator, and an automatic remeshing strategy was adopted to achieve a solution satisfying a preset quality. Examples of the performance of the error estimator in adaptive mesh refinement are presented. The adaptive finite-element scheme presented in this study has proved to he an effective technique in minimizing errors in finite-element solutions for a given problem, in particular those of complex geometries. As an example, numerical solutions are presented for the case of a charged spherical particle at various distances from a charged cylindrical pore in a charged planar surface. Such a scheme provides a quantification of the significance of electrostatic interactions for an important industrial technology-membrane separation processes.

KW - Adaptivity

KW - Boltzman equation

KW - Finite element

KW - Membrane

KW - Poisson

KW - Sphere-pore interaction

UR - http://www.scopus.com/inward/record.url?scp=0030777609&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0030777609&partnerID=8YFLogxK

U2 - 10.1006/jcis.1996.4705

DO - 10.1006/jcis.1996.4705

M3 - Article

VL - 187

SP - 363

EP - 374

JO - Journal of Colloid and Interface Science

JF - Journal of Colloid and Interface Science

SN - 0021-9797

IS - 2

ER -