From O(kN) to O(N): A Fast Complex-Valued Eigenvalue Solver For Large-Scale On-Chip Interconnect Analysis

In general, the optimal computational complexity of Arnoldi iteration is O(kN) for solving a generalized eigenvalue problem, with k being the number of dominant eigenvalues and N the matrix size. In this work, we reduce the computational complexity of the Arnoldi iteration from O(kN) to O(N), thus paving the way for full-wave extraction of very large-scale onchip interconnects, the k of which is hundreds of thousands. Numerical and experimental results have demonstrated the accuracy and efficiency of the proposed fast eigenvalue solver. Index Terms — Arnoldi iteration, generalized eigenvalue problem, on-chip interconnects, full-wave analysis, frequency domain.