Third M.I.T. Conference on Computational Fluid and Solid Mechanics June 14–17, 2005  

A two-dimensional floating random-walk algorithm for the solution of the nonlinear Poisson-Boltzmann equation: application to the modeling of plasma sheaths

K. Chatterjeea,*, J. Poggieb
aMassachusetts Institute of Technology, Laboratory for Electromagnetic and Electronic Systems, MA 02139, USA  bAir Force Research Laboratory, Wright-Patterson Air Force Base, OH 45433, USA

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This paper presents a new, meshless and inherently parallelizable floating random-walk (FRW) algorithm for the solution of the two-dimensional nonlinear Poisson-Boltzmann (NPB) equation. Historically, the FRW method has not been applied to nonlinear problems of significance, which can be attributed to the absence of Green's functions. This problem has been remedied in our work by a novel use of iterative perturbation theory. Our past work involved the FRW solution of the NPB equation in one dimension. In this work, we extend the algorithm to two dimensions and excellent agreement has been obtained with a finite-difference based solution. The application area of interest is the modeling of plasma sheaths.

Keywords:  Floating random-walk; Stochastic methods; Nonlinear Poisson-Boltzmann equation; Plasma sheaths

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