A simple but numerically unmanageable frequency-domain waveguide discontinuity problem

It is shown that it is possible to define an almost trivial frequency-domain waveguide discontinuity problem which cannot be reliably solved by frequency-domain numerical simulators. This happens when among the media involved in the problems of interest there are metamaterials described in terms of effective constitutive parameters. As a consequence, the results of (frequency-domain) numerical simulators should not be taken for granted unless restrictive hypotheses on the media involved are taken into account.