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

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.