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Title: A new Green's function Monte Carlo algorithm for the solution of the two-dimensional nonlinear Poisson–Boltzmann equation: Application to the modeling of the communication breakdown problem in space vehicles during re-entry

The objective of this paper is the exposition of a recently-developed, novel Green's function Monte Carlo (GFMC) algorithm for the solution of nonlinear partial differential equations and its application to the modeling of the plasma sheath region around a cylindrical conducting object, carrying a potential and moving at low speeds through an otherwise neutral medium. The plasma sheath is modeled in equilibrium through the GFMC solution of the nonlinear Poisson–Boltzmann (NPB) equation. The traditional Monte Carlo based approaches for the solution of nonlinear equations are iterative in nature, involving branching stochastic processes which are used to calculate linear functionals of the solution of nonlinear integral equations. Over the last several years, one of the authors of this paper, K. Chatterjee has been developing a philosophically-different approach, where the linearization of the equation of interest is not required and hence there is no need for iteration and the simulation of branching processes. Instead, an approximate expression for the Green's function is obtained using perturbation theory, which is used to formulate the random walk equations within the problem sub-domains where the random walker makes its walks. However, as a trade-off, the dimensions of these sub-domains have to be restricted by the limitationsmore » imposed by perturbation theory. The greatest advantage of this approach is the ease and simplicity of parallelization stemming from the lack of the need for iteration, as a result of which the parallelization procedure is identical to the parallelization procedure for the GFMC solution of a linear problem. The application area of interest is in the modeling of the communication breakdown problem during a space vehicle's re-entry into the atmosphere. However, additional application areas are being explored in the modeling of electromagnetic propagation through the atmosphere/ionosphere in UHF/GPS applications.« less
Authors:
 [1] ;  [2] ;  [3] ;  [4]
  1. Strategic and Military Space Division, Space Dynamics Laboratory, North Logan, UT 84341 (United States)
  2. (United States)
  3. Air Force Research Laboratory, Kirtland AFB, NM 87117 (United States)
  4. Department of Electrical Engineering, The University of Tulsa, Tulsa, OK 74104 (United States)
Publication Date:
OSTI Identifier:
22382138
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Computational Physics; Journal Volume: 276; Other Information: Copyright (c) 2014 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGORITHMS; APPROXIMATIONS; ATMOSPHERES; BOLTZMANN EQUATION; BRANCHING RATIO; COMMUNICATIONS; GLOBAL POSITIONING SYSTEM; GRAPH THEORY; GREEN FUNCTION; IONOSPHERE; ITERATIVE METHODS; MATHEMATICAL SOLUTIONS; MONTE CARLO METHOD; NONLINEAR PROBLEMS; PERTURBATION THEORY; PLASMA SHEATH; REENTRY; SPACE VEHICLES; STOCHASTIC PROCESSES; TWO-DIMENSIONAL CALCULATIONS