Contents I. Introduction
In recent years two powerful concepts have emerged in computational electromagnetics that significantly improve the efficiency of grid based numerical methods such as Finite Differences (FD) and Finite Elements (FE). The first one is the Fast Frequency Sweep (FFS) [6] that gives wideband characteristics of a circuit at a cost comparable to the cost of single frequency point analysis, and the other one are macromodels [1], [4] which are capable of capturing complex field behavior in selected areas of finely meshed computational space with fewer variables than the underlaying scheme. An additional feature of macromodels is that one can avoid adverse effect of local fine meshing on convergence (for frequency domain) [3] or stability (for time-domain) [2] of iterative algorithms used. Both concepts rely on Model Order Reduction (MOR) techniques such as the PVL (Pade via Lanczos), PRIMA (Passive Reduced-Order Interconnect Macromodeling Algorithm) and ENOR (Efficient Nodal Order Reduction) that find a small set of orthogonal vectors which span the solution space in the limited frequency range. Vectors forming the basis are computed by processing block moments (LU decomposition, othogonalization) of coefficient matrices. Processing of block moments becomes less efficient as the size of the matrix involved increases, so the size of the problems that can be handled efficiently is limited to about tens of thousends of unknowns. Moreover, the coefficient matrices have to be frequency independent. This requirement imposes a limit on the applicability of MOR techniques and so far has been preventing nesting different macromodels and simultaneous use of FFS with macromodels.
