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Preliminary Investigations of a Stochastic Method to solve Electrostatic and Electrodynamic Problems

by Kolluru, Sethu Hareesh

Abstract (Summary)
A stochastic method is developed, implemented and investigated here for solving Laplace, Poisson's, and standard parabolic wave equations. This method is based on the properties of random walk, diffusion process, Ito formula, Dynkin formula and Monte Carlo simulations. The developed method is a local method i:e: it gives the value of the solution directly at an arbitrary point rather than extracting its value from complete field solution and thus is inherently parallel. Field computation by this method is demonstrated for electrostatic and electrodynamic propagation problems by considering simple examples and numerical results are presented to validate this method. Numerical investigations are carried out to understand efficacy and limitations of this method and to provide qualitative understanding of various parameters involved in this method.
Bibliographical Information:

Advisor:

School:University of Massachusetts Amherst

School Location:USA - Massachusetts

Source Type:Master's Thesis

Keywords:random walk brownian motion parabolic wave equation electrostatic electrodynamic electromagnetics engineering

ISBN:

Date of Publication:01/01/2008

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