Treffer: A two-dimensional stochastic algorithm for the solution of the non-linear Poisson-Boltzmann equation : validation with finite-difference benchmarks

Title:
A two-dimensional stochastic algorithm for the solution of the non-linear Poisson-Boltzmann equation : validation with finite-difference benchmarks
Authors:
CHATTERJEE, Kausik, POGGIE, Jonathan
Source:
International journal for numerical methods in engineering. 66(1):72-84
Publisher Information:
Chichester: Wiley, 2006.
Publication Year:
2006
Physical Description:
print, 19 ref
Original Material:
INIST-CNRS
Subject Terms:
Geology, Géologie, Mathematics, Mathématiques, Mechanics acoustics, Mécanique et acoustique, Physics, Physique, Sciences exactes et technologie, Exact sciences and technology, Physique, Physics, Generalites, General, Méthodes mathématiques en physique, Mathematical methods in physics, Techniques de calcul, Computational techniques, Physique statistique, thermodynamique, et systèmes dynamiques non linéaires, Statistical physics, thermodynamics, and nonlinear dynamical systems, Mécanique statistique classique, Classical statistical mechanics, Théorie cinétique, Kinetic theory, Domaines classiques de la physique (y compris les applications), Fundamental areas of phenomenology (including applications), Physique des gaz, des plasmas et des decharges electriques, Physics of gases, plasmas and electric discharges, Physique des gaz, Physics of gases, Approche probabiliste, Probabilistic approach, Enfoque probabilista, Corps flottant, Floating body, Cuerpo flotante, Dispositif semiconducteur, Semiconductor devices, Effet non linéaire, Non linear effect, Efecto no lineal, Equation Boltzmann, Boltzmann equation, Equation Poisson, Poisson equation, Equation différences, Difference equations, Equation linéarisée, Linearized equation, Ecuación linearizada, Fonction Green, Green function, Gaine plasma, Plasma sheaths, Marche aléatoire, Random walk, Modélisation, Modelling, Méthode différence finie, Finite difference method, Théorie cinétique, Kinetic theory, Monte Carlo, floating random walk algorithm, modelling of biomolecular structure and dynamics, modelling of plasma sheaths, non-linear Poisson- Boltzmann equation, semiconductor device modelling, stochastic algorithm
Document Type:
Fachzeitschrift Article
File Description:
text
Language:
English
Author Affiliations:
Department of Electrical and Computer Engineering. Cooper Union, New York, NY 10003-7120, United States
Laboratory for Electromagnetic and Electronic Systems, Massachusetts Institute of Technology, Cambridge, MA 02139-4307, United States
Computational Sciences Center, Air Force Research Laboratory. Wright-Patterson AFB, OH 45433-7512, United States
ISSN:
0029-5981
Access URL:
http://pascal-francis.inist.fr/vibad/index.php?action=search&terms=17589391
Rights:
Copyright 2006 INIST-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Mathematics

Physics of gases, plasmas and electric discharges

Theoretical physics
Accession Number:
edscal.17589391
Database:
PASCAL Archive

Weitere Informationen

This paper presents a two-dimensional floating random walk (FRW) algorithm for the solution of the non-linear Poisson-Boltzmann (NPB) equation. In the past, the FRW method has not been applied to the solution of the NPB equation which can be attributed to the absence of analytical expressions for volumetric Green's functions. Previous studies using the FRW method have examined only the linearized Poisson-Boltzmann equation. No such linearization is needed for the present approach. Approximate volumetric Green's functions have been derived with the help of perturbation theory, and these expressions have been incorporated within the FRW framework. A unique advantage of this algorithm is that it requires no discretization of either the volume or the surface of the problem domains. Furthermore, each random walk is independent, so that the computational procedure is highly parallelizable. In our previous work, we have presented preliminary calculations for one-dimensional and quasi-one-dimensional benchmark problems. In this paper, we present the detailed formulation of a two-dimensional algorithm, along with extensive finite-difference validation on fully two-dimensional benchmark problems. The solution of the NPB equation has many interesting applications, including the modelling of plasma discharges, semiconductor device modelling and the modelling of biomolecular structures and dynamics.