Statistically inspired multi-shift Arnoldi projection for on-chip interconnects

Malik, Rahila; Alam, Mehboob; Muhammad, Shah; Hussain, Rashida; Ali, Asghar; Akram, Namra; Duraihem, Faisal Z.; Haq, Anwar Ul

doi:10.1016/j.matcom.2021.05.025

Cited by 3 publications

(4 citation statements)

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“…It is important here to formally define Spectral Zeros (SZs). They are zeros of the follwing square system (7), which are the eigenvalues of the matrix (7) This is essentially the motivation for our proposed GSP method to preserve frequency-selective passivity. The method divides the frequency limits into regular intervals and selects the stable spectral zeros, which are guassianly distributed in the area of interest.…”

Section: Passivity Preserving Mor Using Statistical Distributionmentioning

confidence: 99%

“…The on-chip devices scaling and interconnects resulted in an exponential rise in design complexity with increased simulation time [2], [3]. While creating largescale systems, the physical behavior can often be simplified and represented by a system of mathematical equations [4], [5], [6], [7]. Modeling of the on-chip devices and interconnect often resulted in a large-scale system of differential equations, thereby making it essential to replace it with a lower-order approximation for testing and design verification.…”

Section: Introductionmentioning

confidence: 99%

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Statistically Inspired Passivity Preserving Model Order Reduction

et al. 2023

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The continuous scaling of the on-chip devices and interconnects increases the complexity of the design space and becomes a crucial factor in the fabrication of modern integrated circuits. The ever decreasing of interconnect pitch along with process enhancement into the nanometer regime had shifted the paradigm from a device-dominated to an interconnect-dominated methodology. In the design methodology, Model Order Reduction (MOR) reduces the size of large-scale simulation of on-chip interconnect to speed up the performance of design tools and chip validation. In approximating the original system, the passivity preserving MOR technique of using spectral zeros as positive real interpolation points preserves the stability and passivity of the system. In this work, statistical distribution techniques are proposed for the selection of spectral zeros. The proposed method is based on using the gaussian, uniform, binomial, and weibull distributions to select spectral zeros to better match moments with the least absolute error between the original and reduced-order systems. The results show that the reduced-order model developed using the Gaussian distributed Spectral zeros Projection (GSP) method offers higher accuracy and numerical stability compared to other distributions.INDEX TERMS Statistical distribution, model order reduction, passivity preserving, spectral zeros, on-chip interconnects, computer aided design.

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Section: Passivity Preserving Mor Using Statistical Distributionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Statistically Inspired Passivity Preserving Model Order Reduction

et al. 2023

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“…In our proposed model, the frequency selection is performed by normally distributing the frequency of interest and selecting the interpolation points, which follow a normal distribution in the reduced norm sense. The selected frequency becomes the interpolation point for constructing the projection matrix V [33], [34]. The normal Gaussian kernel can be defined as…”

Section: A Pseudocode For Soar-gkmentioning

confidence: 99%

“…Example 3.1: Consider a second-order dynamical system of an inductor with n = 5. The state representation can be written as [33], [34],…”

Section: A Pseudocode For Soar-gkmentioning

confidence: 99%

Second-Order Arnoldi Reduction Using Weighted Gaussian Kernel

et al. 2022

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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.

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