ABSTRACT
To apply Monte Carlo methods (MCMs) to solve the partial differential equations (PDEs) encountered in electromagnetics, we must first convert the differential equations into their finite difference equivalents. This requires familiarity with the finite difference method (FDM). The first step in solving an electromagnetic boundary value problem using finite differences is to obtain difference equations. The iterative methods are generally used to solve a large system of simultaneous equations. An iterative method for solving equations is one in which a first approximation is used to calculate a second approximation, which in turn is used to calculate the third approximation, and so on. This chapter discusses the successive over-relaxation (SOR) iterative method. The most common approach to the finite difference solution of Maxwell's equations is the finite difference time domain (FDTD) method. A basic difficulty encountered in applying the FDTD method to problems involving open or unbounded geometries is that in the domain the field is infinite.
