Advantages and Disadvantages of Various Numerical Methods :

• For Computing the electric fields, various methods have been used, viz. Finite Difference Method, Finite Element Method, Charge Stimulation Method.

• Each of these methods has its own advantages for solving a particular problem.

• With the FDM, the numerical evaluation of the difference equation is simple but time consuming. For treating a given field problem, it is necessary to sub-divide the finite plane of the field problem into a predominantly regular net of polygons which is supplemented with irregular elements at the boundaries. However, in this method, all difference equations are approximation to the field equation by neglecting the higher order terms. Thus, the resulting error can be large.

• On the other hand, Finite Element Method is a very general method and has been used for solving a variety of problems. Any non-linearity/inhomogeneity can be modelled and the solution will be available on the entire surface of the domain. Material interface conditions are automatically satisfied. However, it needs a powerful graphic user interface for processing.

• Open geometry does not pose any problem with the Charge Stimulaion Method since the surface of the conductor is the only one that is discretized. In addition, as the solution satisfies the Laplace's/Poisson's equation, it will be very smooth, and always gives a small due to the application of superposition principle, non-linearities and non-homogeneity cannot be modelled using this method.

• Of the above methods, the choice of a particular method depends on the specific problem on hand. In general, the construction of Finite Element model requires considerable effort. Since the entire field region should be meshed. While the Charge Stimulation method require only the outer surface of the electrode and the outer layer of the dielectric to be meshed. In practice, an important difference between the various numerical methods in that the Finite Element Method can be used only with fields which are bounded while the Charge Simulation method can also deal with unbounded fields.