Solution of Axisymmetric Inhomogeneous Problems with the Markov Chain Monte Carlo

Abstract

With increasing complexity of EM problems, 1D and 2D axisymmetric approximations in p, z plane are sometimes necessary to quickly solve difficult symmetric problems using limited data storage and within shortest possible time. Inhomogeneous EM problems frequently occur in cases where two or more dielectric media, separated by an interface, exist and could pose challenges in complex EM problems. Simple, fast and efficient numerical techniques are constantly desired. This paper presents the application of simple and efficient Markov Chain Monte Carlo (MCMC) to EM inhomogeneous axisymmetric Laplace’s equations. Two cases are considered based on constant and mixed boundary potentials and MCMC solutions are found to be in close agreement with the finite difference solutions.

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

“…The absorption probability matrix B is thus (16) where matrix is the probability of moving from non-absorbing node to absorbing node j. The B matrix is stochastic and it is given as (17) Thus, (18) where and are the free and fixed nodes potentials respectively.…”