The bilinear method:a new stability-preserving order reduction approach

A new way of reducing the order of linear system transfer functions is presented. It guarantees stability in the approximation of stable systems and differs from existing stability-preserving methods by taking into account whole system parameter information when obtaining the approximate poles, not just that of the system poles. It uses a bilinear transformation in the process, which renders the method more flexible than traditional techniques. Examples are given to highlight the advantages of the new approach

Efficient wideband electromagnetic scattering computation for frequency dependent lossy dielectrics using WCAWE

This paper presents a model order reduction algorithm for the volume electric field integral equation (EFIE) formulation, that achieves fast and accurate frequency sweep calculations of electromagnetic wave scattering. An inhomogeneous, two-dimensional, lossy dielectric object whose material is characterized by a complex permittivity which varies with frequency is considered. The variation in the dielectric properties of the ceramic BaxLa4Ti 2+xO 12+3x in the <1 GHz frequency range is investigated for various values of x in a frequency sweep analysis. We apply the well-conditioned asymptotic waveform evaluation (WCAWE) method to circumvent the computational complexity associated with the numerical solution of such formulations. A multipoint automatic WCAWE method is also demonstrated which can produce an accurate solution over a much broader bandwidth. Several numerical examples are given on order to illustrate the accuracy and robustness of the proposed methods

Shift-and-scale model reduction:an alternative stability-preserving approach

A new stability-preserving model order-reduction method is presented for continuous-time systems. It makes use of the relatively new idea of transformed whole-system parameter matching for calculating the poles of the reduced-order transfer function. This has the advantage of using more of the system information than traditional methods in the approximation of the poles. The method is seen to be flexible and computationally attractive, relying only on readily available algorithms. It is based on a shift-and-scale transformation of the transfer function before applying the order-reduction process. Further, it is shown to be a viable alternative to existing stability-preserving techniques. Some examples illustrate the method

Model-order reduction techniques for the numerical solution of electromagnetic wave scattering problems

It is the aim of this work to contribute to the development of model-order reduction (MOR) techniques for the field of computational electromagnetics in relation to the electric field integral equation (EFIE) formulation. The ultimate goal is to enable a fast-sweep analysis. In a fast-sweep problem, some parameter on which the original problem depends is varying and the problem must be solved as the parameter changes over a desired parameter range. The complexity of the original model prohibits its direct use in simulation to compute the results at every required point. However, one can use MOR techniques to generate reduced-order models (ROMs), which can be rapidly solved to characterise the parameter-dependent behaviour of the system over the entire parameter range. This thesis focus is to implement robust, fast and accurate MOR techniques with strict error controls, for application with varying parameters, using the EFIE formulations. While these formulations result in matrices that are significantly smaller relative to differential equation-based formulations, the matrices resulting from discretising integral equations are very dense. Consequently, EFIEs pose a difficult proposition in the generation of low-order accurate reduced order models. The MOR techniques presented in this thesis are based on the theory of Krylov projections. They are widely accepted as being the most flexible and computationally efficient approaches in the generation of ROMs. There are three main contributions attributed to this work. ² The formulation of an approximate extension of the Arnoldi algorithm to produce a ROM for an inhomogeneous contrast-sweep and source-sweep analysis. ² Investigation of the application of the Well-Conditioned Asymptotic Waveform Evaluation (WCAWE) technique to problems in which the system matrix has a nonlinear parameter dependence for EFIE formulations. ² The development of a fast full-wave frequency sweep analysis using the WCAWE technique for materials with frequency-dependent dielectric properties

An adaptive-order rational Arnoldi method for model-order reductions of linear time-invariant systems

AbstractThis work proposes a model reduction method, the adaptive-order rational Arnoldi (AORA) method, to be applied to large-scale linear systems. It is based on an extension of the classical multi-point Padé approximation (or the so-called multi-point moment matching), using the rational Arnoldi iteration approach. Given a set of predetermined expansion points, an exact expression for the error between the output moment of the original system and that of the reduced-order system, related to each expansion point, is derived first. In each iteration of the proposed adaptive-order rational Arnoldi algorithm, the expansion frequency corresponding to the maximum output moment error will be chosen. Hence, the corresponding reduced-order model yields the greatest improvement in output moments among all reduced-order models of the same order. A detailed theoretical study is described. The proposed method is very appropriate for large-scale electronic systems, including VLSI interconnect models and digital filter designs. Several examples are considered to demonstrate the effectiveness and efficiency of the proposed method