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Title: Using pseudo transient continuation and the finite element method to solve the nonlinear Poisson-Boltzmann equation

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, unstructured-grid, 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.

Authors:
; ;
Publication Date:
Research Org.:
Lawrence Livermore National Lab., CA (US)
Sponsoring Org.:
US Department of Energy (US)
OSTI Identifier:
15005762
Report Number(s):
UCRL-JC-139342-REV-1
TRN: US200324%%246
DOE Contract Number:  
W-7405-ENG-48
Resource Type:
Conference
Resource Relation:
Conference: 4th International Modeling and Simulation of Microsystems MSM 2001 Conference, Hilton Head Island, SC (US), 03/19/2001--03/21/2001; Other Information: PBD: 27 Dec 2000
Country of Publication:
United States
Language:
English
Subject:
99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; BOUNDARY CONDITIONS; DIFFUSION; ELECTROSTATICS; FINITE ELEMENT METHOD; MICROSCOPY; PLATES; PROBES; SIMULATION; TRANSIENTS

Citation Formats

Shestakov, A I, Milovich, J L, and Noy, A. Using pseudo transient continuation and the finite element method to solve the nonlinear Poisson-Boltzmann equation. United States: N. p., 2000. Web.
Shestakov, A I, Milovich, J L, & Noy, A. Using pseudo transient continuation and the finite element method to solve the nonlinear Poisson-Boltzmann equation. United States.
Shestakov, A I, Milovich, J L, and Noy, A. Wed . "Using pseudo transient continuation and the finite element method to solve the nonlinear Poisson-Boltzmann equation". United States. https://www.osti.gov/servlets/purl/15005762.
@article{osti_15005762,
title = {Using pseudo transient continuation and the finite element method to solve the nonlinear Poisson-Boltzmann equation},
author = {Shestakov, A I and Milovich, J L and Noy, A},
abstractNote = {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, unstructured-grid, 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.},
doi = {},
journal = {},
number = ,
volume = ,
place = {United States},
year = {2000},
month = {12}
}

Conference:
Other availability
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