A Fast Recycling GMRES Method With Smart Frequency Sweeping for Efficient Periodic Small-Signal Analysis

The periodic small-signal analysis, such as periodic AC (PAC) and noise (PNoise) simulation, has historically been very computationally intensive, particularly when dealing with a large number of frequency points. This paper introduces a new iterative approach that utilizes Krylov subspace recycling technology to enable fast large-scale small-signal analysis. The method involves reusing the Krylov subspace generated during the solution of previous frequencies to expedite the convergence of the iterative solution at subsequent frequencies. Specifically, the paper outlines a recycling method based on the GMRES formulation, which is more efficient and robust compared to the previous recycling method based on the GCR formulation. Additionally, a method for constructing a better frequency sweeping order is presented to further reduce the total number of iterations in the subspace recycling process. The effectiveness of the proposed method is demonstrated through numerical results.