Pole-clustering and rational-interpolation techniques for simplifying distributed systems

A simple approach is presented to simplify a distributed system by further reducing the order of the rational function obtained from conventional reduced-order modeling (ROM) techniques. The method uses pole-clustering and rational-interpolation techniques to determine a low-order model from the high-order intermediate model constructed by multipoint ROM methods. The complexity of this intermediate model is reduced by clustering the poles using an inverse distance measure (IDM) criterion and by calculating fewer poles, applying rational interpolation on the data generated from the original model. The corresponding residues are then determined by fitting the frequency response of the system over a frequency range. The proposed procedure is computationally inexpensive and less sensitive to numerical instability. To illustrate the validity of the method, examples of frequency- and time-domain simulations of an RLCG transmission line and a network representation of a three-dimensional (3-D) patch antenna structure are given