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SMP-RCR: A Sparse Multipoint Moment Matching Method for RC Reduction

Siyuan Yin, Yuncheng Xu, Lin Liu, Fan Yang, Xuan Zeng, Chengtao An, Yangfeng Su

TL;DR

This work tackles the challenge of model order reduction for large multi-port RC circuits by introducing SMP-RCR, a sparse multipoint moment matching framework. It develops a two-pronged strategy: (i) a multipoint moment matching theory that decouples ports and preserves selected internal nodes through congruence and orthogonal transformations, and (ii) sparsity control and deflation techniques that keep the reduced model sparse without sacrificing high-order moment matching. The method achieves superior high-frequency accuracy compared to SIP and accelerates simulation relative to TurboMOR while maintaining similar precision and structure. Practically, SMP-RCR enables efficient post-layout RC reduction for circuits with many ports by delivering sparse yet accurate reduced models suitable for fast time-domain or frequency-domain simulation.

Abstract

In post--layout circuit simulation, efficient model order reduction (MOR) for many--port resistor--capacitor (RC) circuits remains a crucial issue. The current mainstream MOR methods for such circuits include high--order moment matching methods and elimination methods. High-order moment matching methods--characterized by high accuracy, such as PRIMA and TurboMOR--tend to generate large dense reduced-order systems when the number of ports is large, which impairs the efficiency of MOR. Another common type of MOR method for many--port circuits is based on Gaussian elimination, with the SIP method as a representative. The main limitation of this method lies in the inadequate matching of high--order moments. In this paper, we propose a sparse multipoint moment matching method and present comprehensive theoretical analysis results regarding the multi--frequency high--order moment matching property. Meanwhile, to enhance the algorithm's efficiency, sparse control and deflation techniques are introduced to further optimize the algorithm. Numerical experiments demonstrated that, compared to SIP, the accuracy is improved by more than two orders of magnitude at high frequency points without adding many extra linear components. Compared to TurboMOR methods, our method achieves a speed improvement of more than twice while maintaining the same level of precision.

SMP-RCR: A Sparse Multipoint Moment Matching Method for RC Reduction

TL;DR

This work tackles the challenge of model order reduction for large multi-port RC circuits by introducing SMP-RCR, a sparse multipoint moment matching framework. It develops a two-pronged strategy: (i) a multipoint moment matching theory that decouples ports and preserves selected internal nodes through congruence and orthogonal transformations, and (ii) sparsity control and deflation techniques that keep the reduced model sparse without sacrificing high-order moment matching. The method achieves superior high-frequency accuracy compared to SIP and accelerates simulation relative to TurboMOR while maintaining similar precision and structure. Practically, SMP-RCR enables efficient post-layout RC reduction for circuits with many ports by delivering sparse yet accurate reduced models suitable for fast time-domain or frequency-domain simulation.

Abstract

In post--layout circuit simulation, efficient model order reduction (MOR) for many--port resistor--capacitor (RC) circuits remains a crucial issue. The current mainstream MOR methods for such circuits include high--order moment matching methods and elimination methods. High-order moment matching methods--characterized by high accuracy, such as PRIMA and TurboMOR--tend to generate large dense reduced-order systems when the number of ports is large, which impairs the efficiency of MOR. Another common type of MOR method for many--port circuits is based on Gaussian elimination, with the SIP method as a representative. The main limitation of this method lies in the inadequate matching of high--order moments. In this paper, we propose a sparse multipoint moment matching method and present comprehensive theoretical analysis results regarding the multi--frequency high--order moment matching property. Meanwhile, to enhance the algorithm's efficiency, sparse control and deflation techniques are introduced to further optimize the algorithm. Numerical experiments demonstrated that, compared to SIP, the accuracy is improved by more than two orders of magnitude at high frequency points without adding many extra linear components. Compared to TurboMOR methods, our method achieves a speed improvement of more than twice while maintaining the same level of precision.
Paper Structure (19 sections, 1 theorem, 107 equations, 16 figures, 4 tables)

This paper contains 19 sections, 1 theorem, 107 equations, 16 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. RC Reduction and Moment Matching
  4. TurboMOR-RC
  5. Multipoint Moment Matching Model Order Reduction Framework
  6. Matching two points
  7. Matching more than two points
  8. Moment Matching Analysis
  9. Algorithm Implementation
  10. Sparsity Control
  11. Deflation
  12. Implementation
  13. Numerical Results
  14. Verify Accuracy
  15. Verify Deflation
  16. ...and 4 more sections

Key Result

Theorem 1

The reduced system (Reduced_System) matches the first $2q(s_i)$ moments of the original system (original_system) at $s_i$, $i=1,2,\cdots,m$.

Figures (16)

  • Figure 1: Nonzero Elements of the Reduced Conductance Matrix in ADC_Net_304
  • Figure 2: Nonzero Elements of the Reduced Capacitance Matrix in ADC_Net_304
  • Figure 3: Nonzero of the Conductance Matrix without Deflation in ADC_Net_27
  • Figure 4: Nonzero of the Capacitance Matrix without Deflation in ADC_Net_27
  • Figure 5: Nonzero of Conductance Matrix with Deflation in ADC_Net_27
  • ...and 11 more figures

Theorems & Definitions (2)

  • Theorem 1
  • Proof 1