Applying absorbing Markov chains to solve Poisson's equation in inhomogeneous regions

Abstract

Monte Carlo methods are generally known for solving field problems one point at a time unlike other numerical methods such as the finite difference and finite element methods which provide simultaneously the solution at all of the grid nodes. This work presents an absorbing Markov chain method to solve Poisson's equation with Dirichlet boundary conditions for intractable inhomogeneous problems.