$\mathcal {H}$-Matrix Accelerated Contour Integral Method for Modeling Multiconductor Transmission Lines

An efficient algorithm based on the contour integral method (CIM) is presented in this letter for the modeling of lossy multiconductor transmission lines. Different from the volume integral equation, the CIM only discretizes the contour of the cross section of each conductor, which significantly reduces the number of unknowns in the resultant system equations. The solution of the CIM is accelerated by the hierarchical-matrix (
$\mathcal {H}$
-matrix) algorithm for the extraction of the per-unit-length resistance and inductance parameters of massively coupled transmission lines. The procedures for the
$\mathcal {H}$
-matrix-based solution are optimized to keep its optimal computational complexity. The numerical results from the proposed method agree well with those from the commercial software. The complexities of CPU time and memory cost for the construction of the
$\mathcal {H}$
-matrices are both
$O(N\log {}N)$
, and the complexity of the solution for parameter extraction is
$O(N\log ^2{}N)$
.