Spatial error criterion for discrete complex image method

Although DCIM is very robust and efficient to obtain spatial-domain Green's functions from their spectral-domain counterparts in planar media, the method suffers from the lack of an error metric ensuring the accuracy of the end result, which deters CAD developers and engineers from using it in the development of commercial tools. To remedy this shortcoming of DCIM, a weighted 2-norm of the error in the spatial domain is defined and its mapping to the spectral domain is derived and proposed as the metric to be used in DCIM. In addition, the leakage problem of the multi-level implementations of DCIM is also eliminated. The resulting metric is implemented on the latest three-level DCIM and the proposed three-level DCIM is verified on a typical planar layered geometry.