Using Pseudo Transient Continuation and the Finite Element Method to Solve the Nonlinear Poisson-Boltzmann Equation

	Nanotech 2001 Vol. 1 Technical Proceedings of the 2001 International Conference on Modeling and Simulation of Microsystems Chapter 3: Compact Modeling and Model Order Reduction
	Using Pseudo Transient Continuation and the Finite Element Method to Solve the Nonlinear Poisson-Boltzmann Equation
Authors:	A.I. Shestakov, J.L. Milovich and A. Noy
Affilation:	Lawrence Livermore National Laboratory, US
Pages:	39 - 43
Keywords:	Poisson-Boltzmann, chemical force microscopy, pseudo transient continuation, finite elements
Abstract:	The nonlinear Poisson-Boltzmann (PB) eequation is solved using Pseudo Transient Continuation. The PB solver is constructed by modifying the nonlinear diffusion modeule 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 lineariezes 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.
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ISBN:	0-9708275-0-4
Pages:	638
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