The nucleation of vortices and the resulting structures of vortex arrays in
dilute, trapped, zero-temperature Bose-Einstein condensates are investigat
ed numerically. Vortices are generated by rotating a three-dimensional, ani
sotropic harmonic atom trap. The condensate ground state is obtained by pro
pagating the Gross-Pitaevskii equation in imaginary time. Vortices first ap
pear at a rotation frequency significantly larger than the critical frequen
cy for vortex stabilization, consistent with a critical velocity mechanism
for vortex nucleation. At higher frequencies, the structures of the vortex
arrays are strongly influenced by trap geometry.