Parameterized Model Order Reduction of Electromagnetic Systems Using Multiorder Arnoldi

This paper presents an efficient algorithm to create parametric reduced order models of distributed electromagnetic systems that have arbitrary functions of frequency (due to material properties, boundary conditions, delay elements) and design parameters. The proposed method is based on a multiorder Arnoldi algorithm used to implicitly calculate the moments with respect to frequency and design parameters, as well as the cross-moments. This procedure generates parametric reduced order models that are valid over the desired parameter range without the need to redo the reduction when design parameters are changed. Numerical examples are provided to illustrate the validity of the proposed algorithm.

I. Introduction

To model high-speed integrated and microwave circuits, macromodeling algorithms are often used to convert the partial differential equations describing distributed components into ordinary differential equations [1] [2] [45]. However, due to the complexity of distributed networks, this results in large system of equations, simulation of which is prohibitively CPU expensive. This problem is further compounded when one considers the typical design process which includes optimization and design space exploration and thus requires repeated simulation of the same problem for different design parameters.