Simulating the transient response of a multiconductor transmission line by an extended krylov method

In this paper we present an extended Krylov method to simulate the transient response of multiconductor transmission lines. The extended Krylov space is generated by the transmission line system matrix and its inverse. Loosely speaking, the idea is that early-times are approximated by powers of the system matrix, while late-times are approximated by powers of its inverse. Acting with the system matrix or its inverse on a given vector is an O(p) process, where p is the order of the total system. Moreover, both matrices are so-called J-symmetric matrices and we show that it is possible to generate a J-orthogonal basis of the extended Krylov space via short Lanczos/CG-type recurrence relations.