ABSTRACT
This chapter proposes a simple technique for whole field calculations. The technique basically calculates the transition probabilities using absorbing Markov chains and gives an exact solution unlike other numerical techniques such as finite difference and finite element methods. The chapter begins with a very brief discussion of the regular Monte Carlo method (MCM). It then presents the absorbing Markov chains and shows how they can be used in calculating the potential for the entire region. A Markov process is a type of random process that is characterized by the memoryless property. It is a process evolving in time that remembers only the most recent past and whose conditional probability distributions are time invariant. The ideas presented in the chapter can be extended to solution regions that are inhomogeneous or nonrectangular or both. All it takes is calculating the transition probability. The idea of Markov chain may also be used to solve Poisson's equation and the wave equation.
