Commun. Comput. Phys., 8 (2010), pp. 327-350. Numerical Study of Vortex Interactions in Bose-Einstein Condensation Yanzhi Zhang 1*1 Department of Scientific Computing, Florida State University, Tallahassee, FL 32306-4120, USA. Received 30 June 2009; Accepted (in revised version) 5 October 2009 Available online 12 March 2010 doi:10.4208/cicp.2009.09.104 Abstract The dynamics and interaction of quantized vortices in Bose-Einstein condensates (BECs) are investigated by using the two-dimensional Gross-Pitaevskii equation (GPE) with/without an angular momentum rotation term. If all vortices have the same winding number, they would rotate around the trap center but never collide. In contrast, if the winding numbers are different, their interaction highly depends on the initial distance between vortex centers. The analytical results are presented to describe the dynamics of the vortex centers when $\beta =0$. While if $\beta\neq0$, there is no analytical result but some conclusive numerical findings are provided for the further understanding of vortex interaction in BECs. Finally, the dynamic laws describing the relation of vortex interaction in nonrotating and rotating BECs are presented. Notice: Undefined variable: ams in /var/www/html/issue/abstract/readabs.php on line 163 PACS: 03.75.Kk, 03.75.Lm, 05.30.Jp, 32.80.Pj Key words: Rotating Bose-Einstein condensation, Gross-Pitaevskii equation, angular momentum rotation, vortex interaction, vortex pair, vortex dipole. *Corresponding author. Email: yzhang5@fsu.edu (Y. Zhang)