FlexRC: A Flexible Multi-Point Model Order Reduction Method for Many-Port RC Networks

Jul 16, 2026

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Efficient model order reduction for many-port resistor-capacitor (RC) networks is crucial for post-layout circuit simulation. Existing elimination-based approaches can be limited by fixed frequency points, large reduced orders, or high computational cost. FlexRC introduces flexible multi-point reduction that builds a nonorthogonal projection basis via a modified block rational Arnoldi process, producing a sparse banded reduced model. It provides user-set frequency points, a tolerance-controlled port-reduction strategy, and optional sparsity control. Numerical results on industrial RC and power-grid cases show improved reduction and transient simulation times.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages14

Reading Time35 min

Introduction

Motivation and challenges in RC reduction

Limitations of existing MOR and RC reduction methods

FlexRC approach overview

FlexRC: A Flexible Multi-Point Model Order Reduction Method for Many-Port RC Networks Yuncheng Xu, Siyuan Yin, Lin Liu, Fan Yang, Member, IEEE, Xuan Zeng, Senior Member, IEEE, Chengtao An, and Yangfeng Su arXiv :2607 .05934v1 [ ee ss . SY] 7 Jul 2026 Abstract—Efficient model order reduction for many-port resistor-capacitor (RC) networks is essential in post-layout circuit simulation. Existing high-accuracy elimination-based methods have certain limitations, such as fixed frequency points, large reduced-order models, or high reduction cost. This paper proposes FlexRC, a flexible multi-point model order reduction method for many-port RC networks. FlexRC starts from the same elimination step as previous methods, and then constructsa nonorthogonal projection basis by a modified block rational Arnoldi process to generate a sparse banded reduced model. FlexRC features three adjustable components: user-specified frequency points, a tolerance-controlled port-reduction technique for the internal subsystem, and an optional sparsity-control strategy. We discuss passivity under port-reduction perturbations, analyze moment matching, and provide a conservative error estimate for port reduction. Numerical experiments on industrial RC examples and IBM power-grid examples demonstrate the effectiveness of FlexRC in terms of reduction time and transient simulation time. Index Terms—Many-port RC networks, model order reduction, multi-point moment matching, Krylov subspace methods, port reduction. I. INTRODUCTION In modern IC design, interconnect effects have become a dominant factor in determining whole-chip performance [1]–[3] . Massive parasitic models, especially resistor-capacitor (RC) networks, are extracted and connected to nonlinear devices for post-layout simulation. The large numbers of nodes and ports in RC parasitic networks make direct nonlinear simulation computationally prohibitive and time-consuming. Model order reduction (MOR) is frequently used to speedup the simulation of interconnect circuits. MOR methods applied directly to the full nonlinear system, such as proper orthogonal decomposition (POD) [4]–[6], are computationally expensive. Therefore, RC reduction (RCR), which reduces the linear time-invariant RC networks before nonlinear simulation, has become the mainstream approach. An ideal RC reduction technique should yield accurate reduced-order models while preserving essential properties such as passivity [7], [8] and input-output structure [9] . The primary challenge in RCR lies in the large number of ports connecting the RC network to nonlinear devices. The input-output structure associated with Yuncheng Xu, Siyuan Yin, and Yangfeng Su are with the School of Mathematical Sciences, Fudan University, Shanghai, China. Lin Liu and Chengtao An are with Empyrean, China. Fan Yang and Xuan Zeng are with the State Key Laboratory of Integrated Chips and Systems, College of Integrated Circuits and Micro-Nano Electronics, Fudan University, Shanghai, China. Corresponding authors: Chengtao An (e-mail: [ancht@empyrean.com.cn](ancht@empyrean.com.cn)) and Yangfeng Su (e-mail: [yfsu@fudan.edu.cn](yfsu@fudan.edu.cn)). these ports must be preserved during the reduction process to ensure that the reduced-order model can still be connected to the nonlinear devices for further analysis. High-accuracy MOR methods are difficult to apply to manyport RC networks. TBR-like methods [10]–[12] are limited by slowly decaying Hankel singular values and the high cost of Lyapunov equations [13], while factor division algorithms [14],[15] become impractical when both node and port counts are large. Traditional Krylov subspace methods, notably PRIMA [7],[8], are widely used but become inefficient for many-port networks because the dense projection matrix often produces dense reduced models [16] . Port-compression methods such as SVDMOR [17], ESVDMOR [18], and RECMOR [19] rely on port correlations that are often weak in practical

FAQs

What problem does FlexRC address in post-layout circuit simulation?

FlexRC targets efficient model order reduction for many-port RC networks, where direct simulation becomes too costly due to large node and port counts.

How does FlexRC construct the reduced model basis?

FlexRC builds a nonorthogonal projection basis using a modified block rational Arnoldi process with incomplete orthogonalization, enabling a sparse banded reduced model structure.

What adjustable components does FlexRC provide for accuracy and sparsity?

FlexRC includes user-specified frequency points, a tolerance-controlled port-reduction technique for the internal subsystem, and an optional sparsity-control strategy.

Jul 16, 2026

Upload by Levi