Using pseudo transient continuation and the finite element method to solve the nonlinear poisson-boltzmann equation

A. I. Shestakov, J. L. Milovich, Aleksandr Noy

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

The nonlinear Poisson-Boltzmann (PB) equation is solved using Pseudo Transient Continuation. The PB solver is constructed by modifying the nonlinear diffusion module of a 3D, massively parallel, unstructuredgrid, finite element, radiation-hydrodynamics code. The solver also computes the electrostatic energy and evaluates the force on a user-specified contour. Either Dirichlet or mixed boundary conditions are allowed. The latter specifies surface charges, approximates far-field conditions, or linearizes conditions "regulating" the surface charge. The code may be run in either Cartesian, cylindrical, or spherical coordinates. The potential and force due to a conical probe interacting with a flat plate is computed and the result compared with direct force measurements by chemical force microscopy.

Original languageEnglish (US)
Title of host publication2001 International Conference on Modeling and Simulation of Microsystems - MSM 2001
EditorsM. Laudon, B. Romanowicz
Pages39-43
Number of pages5
StatePublished - 2001
Externally publishedYes
Event2001 International Conference on Modeling and Simulation of Microsystems - MSM 2001 - Hilton Head Island, SC, United States
Duration: Mar 19 2001Mar 21 2001

Other

Other2001 International Conference on Modeling and Simulation of Microsystems - MSM 2001
CountryUnited States
CityHilton Head Island, SC
Period3/19/013/21/01

Fingerprint

Boltzmann equation
Surface charge
Finite element method
Force measurement
Electrostatics
Microscopic examination
Hydrodynamics
Boundary conditions
Radiation

Keywords

  • Chemical force microscopy
  • Finite elements
  • Poisson-Boltzmann
  • Pseudo transient continuation

ASJC Scopus subject areas

  • Engineering(all)

Cite this

Shestakov, A. I., Milovich, J. L., & Noy, A. (2001). Using pseudo transient continuation and the finite element method to solve the nonlinear poisson-boltzmann equation. In M. Laudon, & B. Romanowicz (Eds.), 2001 International Conference on Modeling and Simulation of Microsystems - MSM 2001 (pp. 39-43)

Using pseudo transient continuation and the finite element method to solve the nonlinear poisson-boltzmann equation. / Shestakov, A. I.; Milovich, J. L.; Noy, Aleksandr.

2001 International Conference on Modeling and Simulation of Microsystems - MSM 2001. ed. / M. Laudon; B. Romanowicz. 2001. p. 39-43.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Shestakov, AI, Milovich, JL & Noy, A 2001, Using pseudo transient continuation and the finite element method to solve the nonlinear poisson-boltzmann equation. in M Laudon & B Romanowicz (eds), 2001 International Conference on Modeling and Simulation of Microsystems - MSM 2001. pp. 39-43, 2001 International Conference on Modeling and Simulation of Microsystems - MSM 2001, Hilton Head Island, SC, United States, 3/19/01.
Shestakov AI, Milovich JL, Noy A. Using pseudo transient continuation and the finite element method to solve the nonlinear poisson-boltzmann equation. In Laudon M, Romanowicz B, editors, 2001 International Conference on Modeling and Simulation of Microsystems - MSM 2001. 2001. p. 39-43
Shestakov, A. I. ; Milovich, J. L. ; Noy, Aleksandr. / Using pseudo transient continuation and the finite element method to solve the nonlinear poisson-boltzmann equation. 2001 International Conference on Modeling and Simulation of Microsystems - MSM 2001. editor / M. Laudon ; B. Romanowicz. 2001. pp. 39-43
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