Critical study of the problems in discrete complex image method

The discrete complex image method (DCIM), which is used to get the closed-form Green´s functions in the spatial domain, is critically studied to answer the problems of validity of the method beyond certain distance from the source. The deterioration of the approximation as compared to the exact Green´s functions for moderate to large distances is attributed to several factors, such as introduction of artificial branch points, surface wave poles and not extracting the quasi-static images in two-level approach. Among these issues, the introduction of artificial branch point is discussed in detail, and demonstrated that this can not be the reason for the deterioration of the approximation.