  We describe a simple method of including dissipation in the spin wave band
structure of a periodic ferromagnetic composite, by solving the Landau-Lifshitz
equation for the magnetization with the Gilbert damping term. We use this
approach to calculate the band structure of square and triangular arrays of Ni
nanocylinders embedded in an Fe host. The results show that there are certain
bands and special directions in the Brillouin zone where the spin wave lifetime
is increased by more than an order of magnitude above its average value. Thus,
it may be possible to generate spin waves in such composites decay especially
slowly, and propagate especially large distances, for certain frequencies and
directions in ${\bf k}$-space.
