Generating nearly optimally compact models from Krylov-subspace based reduced-order models

Abstract

Automatic model reduction of chip, package, and board interconnect is now typically accomplished using moment-matching techniques, where the matching procedure is computed in a stable way using orthogonalized or biorthogonalized Krylov-subspace methods. Such methods are quite robust and reasonably efficient, though they can produce reduced-order models that are far from optimally accurate. In particular, when moment-matching methods are applied to generating a reduced-order model for interconnect which exhibits skin effects, the generated models have many more states than necessary. In this paper, we describe our two-step strategy in which we first compute medium-order models using an efficient moment-matching method, and then nearly optimally reduce the medium-order models using truncated balanced realization. Results on a spiral inductor and a package example demonstrate the effectiveness of the two-step approach.

Approximation of Large-Scale Dynamical Systems: An Overview

“…the fundamental connection of Krylov subspace projection methods in linear algebra to the partial realization problem in system theory as laid out in [37,38]; see also [22,33,29,39,74,48]. A closely related approach which has been applied to VLSI circuits can be found in [50]; see also [59].…”

Combining Krylov subspace methods and identification‐based methods for model order reduction

“…This can either be done by a different reduction algorithm as a second step [7,8], or by making the Krylov subspace method more efficient [9]. In [10] a way to stop the iterative process for one column while proceeding with the other ports is pointed out.…”

Model reduction via projection onto nonlinear manifolds, with applications to analog circuits and biochemical systems

“…Our explanation is that it results from the problems brought by aggregation of projection matrices -trivial bases kill the non-trivial ones. By employing a heuristic, 6 TPWL method works for this example, with order reduction from 304 to 144. But even with model size 144, the simulation results of TPWL model, as shown in Fig.…”

“…So far, MOR techniques for linear time invariant systems have been well-developed and widely used, such as Krylov subspace methods [2], [3], TBR methods [4], [5], and the combination of the two [6], [7]. On the other hand, nonlinear systems present a lot of challenges for MOR, and much less robust, efficient, and generallyapplicable methods are available.…”