Markov Chain Monte Carlo Solution of Poisson’s Equation in Axisymmetric Regions

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.