Introduction to numerical techniques in electromagnetics

Finite difference method

The finite difference method is a powerful numerical method for solving partial differential equations. In applying the method of finite differences a problem is defined by:

• A partial differential equation such as Poisson's equation

• A solution region

• Boundary and/or initial conditions.

An FDM method divides the solution domain into finite discrete points and replaces the partial differential equations with a set of difference equations. Thus the solutions obtained by FDM are not exact but approximate. However, if the discritisation is made very fine, the error in the solution can be minimized to an acceptable level. Although an electromagnetic field produces 3-D variations, for the sake of simplicity we shall restrict our discussion to 2-D case only.