Second-Order Arnoldi Reduction Using Weighted Gaussian Kernel

Abstract

Modeling and design of on-chip interconnect continue to be a fundamental roadblock for high-speed electronics. The continuous scaling of devices and on-chip interconnects generates self and mutual inductances, resulting in generating second-order dynamical systems. The model order reduction is an essential part of any modern computer-aided design tool for prefabrication verification in the design of on-chip components and interconnects. The existing second-order reduction methods use expensive matrix inversion to generate orthogonal projection matrices and often do not preserve the stability and passivity of the original system. In this work, a second-order Arnoldi reduction method is proposed, which selectively picks the interpolation points weighted with a Gaussian kernel in the given range of frequencies of interest to generate the projection matrix. The proposed method ensures stability and passivity of the reduced-order model over the desired frequency range. The simulation results show that the combination of multi-shift points weighted with Gaussian kernel and frequency selective projection dynamically generates optimal results with better accuracy and numerical stability compared to existing reduction techniques.INDEX TERMS Interpolation points, Numerical methods, On-Chip Interconnects, Second-order model order reduction, Second-order Arnoldi.

Statistically Inspired Passivity Preserving Model Order Reduction

“…ern design tools for the simulation of on-chip interconnect are numerically expensive and often lack passivity preserving approximation of on-chip systems [8], [9]. In recent decades, complex and large-scale Model Order Reduction (MOR) has been a subject of major interest [10], [11], [12], [13], [14].…”