Recent Advances in Structure-Preserving Model Order Reduction

Abstract

In recent years, model order reduction techniques based on Krylov subspaces have become the methods of choice for generating small-scale macromodels of the large-scale multi-port RCL networks that arise in VLSI interconnect analysis. A difficult and not yet completely resolved issue is how to ensure that the resulting macromodels preserve all the relevant structures of the original large-scale RCL networks. In this paper, we present a brief review of how Krylov subspace techniques emerged as the algorithms of choice in VLSI circuit simulation, describe the current state-of-art of structure preservation, discuss some recent advances, and mention open problems.

Adaptive model reduction technique for large-scale dynamical systems with frequency-dependent damping

“…4. At step 4, the moment-matching property indicates that the ROM using single complex expansion point can only capture the local characteristics within a certain frequency range near such expansion point, otherwise the ROM will become inaccurate beyond that frequency range [30]. Therefore, one may use more than one expansion points to reduce the approximation error of the frequency-dependence in generating the projection basis by enriching the information of subspaces.…”

Rank two perturbations of matrices and operators and operator model for t-transformation of probability measures

“…Note that the coefficient at (z − λ j ′ ) −1 (z − λ j ′′ ) −1 is a polynomial expression in the entries of u, w * , g, h * , cf. (16). Hence, to finish the proof of (b) it is enough to show that for some j ′ , j ′′ and for some u, w * , g, h * the coefficient at (z − λ j ′ ) −1 (z − λ j ′′ ) −1 is nonzero.…”

“…The topic of stability of rank two perturbations of Hamiltonian systems is discussed further in Remark 11. Similar problems occur in modelling electronic circuits [16], where a change in one parameter of the electric network (e.g. cutting the electric transmitter, increasing the capacity of one capacitor, etc.)…”

Acoustic simulation of cavities with porous materials using an adaptive model order reduction technique

“…Thirdly, the adaptive placement of expansion points is typically more appropriate for imaginary s 0 [26]. Even though it is not implemented in the following, a combination of real and imaginary expansion points is also of interest [36]. Substituting Eqs.…”