Error control in the reduced expansion and field testing (REFT) method for MoM matrix thinning

Method of moments (MoM) matrices may contain redundant information, resulting from the dense sampling rates of fields. Therefore, one would like to reduce the amount of data contained in the matrices by effectively slowing down the sampling rates to a level compatible with the physics of the problem, such that sparse rather than dense matrices are produced. The REFT method (Kastner and Nocham 1995, Steinberg and Kastner 1997, and Steinberg et al. 1998) is a spatial domain method which facilitates a slow down of the sampling rate for the generation of a sparse matrix. It generates a single sparse matrix, which is invertible either by direct or iterative solvers. Direct solvers do not share the convergence drawbacks of iterations. A straightforward direct solver, for the case of an N/spl times/N sparse matrix, can be realized with much lower operation count than the O(N/sup 3/) associated with a straightforward Gaussian elimination. The method incorporates a transformation of arbitrary basis and testing functions into a new basis, whereby the active number of both testing and basis functions is reduced to a minimum, thereby the elimination of all the elements except for about 10% of the total. The initial version of the method was presented in a heuristic fashion as the RFT in Kastner and Nocham. The REFT facilitates straightforward operations on any MoM matrix, hence the method is applicable to "legacy codes". Both original and inverted matrices can be thinned. To facilitate this reduction we perform an orthogonal transformation on the basis/testing functions.