An Efficient Krylov Subspace Method to Simulate the Low-Frequency Response of Multiconductor Transmission Lines

Abstract

In this paper we present a Krylov subspace method to efficiently compute the low-frequency response of multiconductor transmission lines. Through a Lanczos-type algorithm we generate so-called spectral Lanczos decomposition approximations on an entire frequency interval of interest. Low frequencies are approximated first, since we use the inverse of the transmission line system matrix in the Lanczos algorithm. Although this inverse is not a sparse matrix, computing its action on a vector still requires an order N amount of work, where N is the total number of unknowns. Moreover, the inverse is a so-called J-symmetric matrix because of reciprocity. This property is exploited in the Lanczos algorithm and approximations are constructed via a three-term recurrence relation. The overall algorithm is therefore very efficient.