Discrete complex image method with spatial error criterion

Abstract

Since its first inception, the discrete complex image method (DCIM) has been criticized for the lack of a proper prediction algorithm of the error incurred during the process. Although the method has been improved and modified several times, not being able to input any prior specification or to get any meaningful assessment on the error deters computer-aided design developers and engineers from using it in the development of commercial software and in-house simulation tools. To remedy this short-coming of the otherwise very popular DCIM, a weighted p-norm of the spatial-domain error is defined, and its mapping to the spectral domain is derived and proposed as the metric to be used in the implementation of the DCIM. Once this metric is incorporated into the latest three-level DCIM algorithm, used for the approximation of the spatial-domain Green's functions, it is observed that the weighted error-energy minimization in the spectral domain becomes equivalent to the one in the spatial domain. In addition to introducing an error criterion to the DCIM, the leakage problem, which is inherent to the semi-independent processing of subregions in multilevel implementations of the DCIM, is also addressed and eliminated, resulting in a further improvement of the algorithm and the end result.