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Model-order reduction is a key technique to do fast simulation of interconnect networks. Among many model-order reduction algorithms, those based on projection methods work quite well. In this paper, we review the projection-based algorithms in two categories. The first one is the coefficient matching algorithms. We generalize the Krylov subspace method on moment matching at a single point, to multipoint moment-matching methods with matching points located anywhere in the closed right-hand side (RHS). of the complex plane, and we provide algorithms matching the coefficients of series expansion-based on orthonormal polynomials and generalized orthonormal basis functions in Hilbert and Hardy space. The second category belongs to the grammian-based algorithms, where we provide efficient algorithm for the computation of grammians and new approximate grammian-based approaches. We summarize some important properties of projection-based algorithms so that they may be used more flexibly.

Traditional timing-variation reduction techniques are only able to decrease gate delay variation by incurring a delay overhead. In this brief, we propose a novel and effective splittingbased variation reduction technique for gates. We developed a new tool called Timing Uncertainty Reduction by Gate Splitting (TURGS), which reduces the timing variations of a circuit and presents little delay overhead at the primary output. Our experimental results show that TURGS achieves up to 20% improvement in timing variation for gates.

This paper proposes a new statistical response surface based power estimation technique. The new approach is able to include a number of parameters such as multiple Vdd, multiple Vth and gate sizing parameters. It has both deterministic ability and statistical ability. The deterministic ability allows the new model to provide optimal design parameters for power reduction. The statistical ability can be used to model the process variation impact on power.

Abstract-This paper proposes a general hierarchical analysis methodology, HiPRIME, to efficiently analyze RLKC power delivery systems. After partitioning the circuits into blocks, we develop and apply the IEKS (Improved Extended Krylov Subspace) method to build the multiport Norton equivalent circuits which transform all the internal sources to Norton current sources at ports. Since there are no active elements inside the Norton circuits, passive or realizable model order reduction techniques such as PRIMA can be applied. The significant speed improvement, 700 times faster than Spice with less than 0.2% error and 7 times faster than a state-of-the-art solver, InductWise, is observed. To further reduce the top-level hierarchy runtime, we develop a second-level model reduction algorithm and prove its passivity.Index Terms-Model order reduction, power distribution, power grid, signal integrity.