# 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}

}