Abstract
The advent of the Monte Carlo methods to the field of EM have seen floating random walk, fixed random walk and Exodus methods deployed to solve Poisson’s equation in rectangular coordinate and axisymmetric solution regions. However, when considering large EM domains, classical Monte Carlo methods could be time-consuming because they calculate potential one point at a time. Thus, Markov Chain Monte Carlo (MCMC) is generally preferred to other Monte Carlo methods when considering whole-field computation. In this paper, MCMC has been applied to solve Poisson’s equation in homogeneous and inhomogeneous axisymmetric regions. The MCMC results are compared with the analytical and finite difference solutions.
Highlights
Poisson’s equation is an elliptic partial differential equation that frequently appears in many scientific problems such as electrostatics, surface reconstruction, gravitational problems, and semiconductors [1]-[2]
Since the introduction of probabilistic method such as Monte Carlo method to the field of electromagnetics, several Monte Carlo methods developed such as floating random walk, fixed random walk and Exodus method have been used to solve Poisson’s equation, notably in rectangular coordinate and axisymmetric solution regions
The Markov Chain Monte Carlo (MCMC) method which is an improvement on the classical Monte Carlo method has been applied to solve Poisson’s equations in axisymmetric region in homogeneous and inhomogeneous regions
Summary
Poisson’s equation is an elliptic partial differential equation that frequently appears in many scientific problems such as electrostatics, surface reconstruction, gravitational problems, and semiconductors [1]-[2]. Poisson’s equation in rectangular coordinate has been extensively studied using different numerical methods [3]-[5]
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