  A great challenge for 21 cm intensity mapping experiments is the strong
foreground radiation which is orders of magnitude brighter than the 21cm
signal. Removal of the foreground takes advantage of the fact that its
frequency spectrum is smooth while the redshifted 21cm signal spectrum is
stochastic. However, a complication is the non-smoothness of the instrument
response. This paper describes the electromagnetic simulation of the Tianlai
cylinder array, a pathfinder for 21 cm intensity mapping experiments. Due to
the vast scales involved, a direct simulation requires large amount of
computing resources. We have made the simulation practical by using a
combination of methods: first simulate a single feed, then an array of feed
units, finally with the feed array and a cylindrical reflector together, to
obtain the response for a single cylinder. We studied its radiation pattern,
bandpass response and the effects of mutual coupling between feed units, and
compared the results with observation. Many features seen in the measurement
result are well reproduced in the simulation, especially the oscillatory
features which are associated with the standing waves on the reflector. The
mutual coupling between feed units is quantified with S-parameters, which
decrease as the distance between the two feeds increases. Based on the
simulated S-parameters, we estimate the correlated noise which has been seen in
the visibility data, the results show very good agreement with the data in both
magnitude and frequency structures. These results provide useful insights on
the problem of 21cm signal extraction for real instruments.
