### 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 language | English (US) |
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Title of host publication | 2001 International Conference on Modeling and Simulation of Microsystems - MSM 2001 |

Editors | M. Laudon, B. Romanowicz |

Pages | 39-43 |

Number of pages | 5 |

State | Published - 2001 |

Externally published | Yes |

Event | 2001 International Conference on Modeling and Simulation of Microsystems - MSM 2001 - Hilton Head Island, SC, United States Duration: Mar 19 2001 → Mar 21 2001 |

### Other

Other | 2001 International Conference on Modeling and Simulation of Microsystems - MSM 2001 |
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Country | United States |

City | Hilton Head Island, SC |

Period | 3/19/01 → 3/21/01 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Engineering(all)

### Cite this

*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.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*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.

}

TY - GEN

T1 - Using pseudo transient continuation and the finite element method to solve the nonlinear poisson-boltzmann equation

AU - Shestakov, A. I.

AU - Milovich, J. L.

AU - Noy, Aleksandr

PY - 2001

Y1 - 2001

N2 - 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.

AB - 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.

KW - Chemical force microscopy

KW - Finite elements

KW - Poisson-Boltzmann

KW - Pseudo transient continuation

UR - http://www.scopus.com/inward/record.url?scp=6344235814&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=6344235814&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:6344235814

SN - 0970827504

SP - 39

EP - 43

BT - 2001 International Conference on Modeling and Simulation of Microsystems - MSM 2001

A2 - Laudon, M.

A2 - Romanowicz, B.

ER -