  We present a new method for the analysis of smoothly varying tapers,
transitions and filters in rectangular waveguides. With this aim, we apply a
Hierarchical Model (HiMod) reduction to the vector Helmholtz equation. We
exploit a suitable coordinate transformation and, successively, we use the
waveguide modes as a basis for the HiMod expansion. We show that accurate
results can be obtained with an impressive speed-up factor when compared with
standard commercial codes based on a three-dimensional finite element
discretization.
