A Multi-Point Moment Matching Approach with Frequency-Aware ROM-Based Criteria for RLCk Model Order Reduction

Model order reduction (MOR) is crucial for efficiently simulating large-scale RLCk models extracted from modern integrated circuits. Among MOR methods, balanced truncation offers strong theoretical error bounds but is computationally intensive and does not preserve passivity. In contrast, moment matching (MM) techniques are widely adopted in industrial tools due to their computational efficiency and ability to preserve passivity in RLCk models. Typically, MM approaches based on the rational Krylov subspace (RKS) are employed to produce reduced-order models (ROMs). However, the quality of the reduction is influenced by the selection of the number of moments and expansion points, which can be challenging to determine. This underlines the need for advanced strategies and reliable convergence criteria to adaptively control the reduction process and ensure accurate ROMs. This article introduces a frequency-aware multi-point MM (MPMM) method that adaptively constructs an RKS by closely monitoring the ROM transfer function. The proposed approach features automatic expansion point selection, local and global convergence criteria, and efficient implementation techniques. Compared to an established MM technique, MPMM achieves up to 16.3× smaller ROMs for the same accuracy, over 99.18% reduction in large-scale benchmarks, and up to 4× faster runtime. These advantages establish MPMM as a strong candidate for integration into industrial parasitic extraction tools.