To my knowledge, I have not read or heard of a specific martial art practiced in the lifetime of the prophet(Peace on him) as is done in this era. However the popular sports of the day included Running, Wrestling, Swimming, Horse riding and archery. I guess this was somewhat sufficient to keep the troops fit enough to wield a sword or shoot an arrow whether standing, running or riding. Whatever type of training method was used, was not(to my knowledge) written about specifically. Perhaps another reader may have a clue to a text that does provide answers relating to the tactical usage of a sword.
Due to the effect of the message of our beloved prophet, many who had accepted the faith were themselves educated and bore skills that greatly benefited the need of the time. The prophet seemed to be not heavily involved in the military complex issues and could have used a lot of advice from his companions. Some where highly skilled prior to accepting Islam.
Please see the following for more : http://www.swordhistory.info/?p=10
You may get an idea about the tribes that influenced the prophet's(Peace on him) means and methods.
Also see: http://en.wikipedia.org/wiki/Rashidun_army . This wiki will probably create an impression about the master sword artists of the day post prophet Muhammad(peace on him).
The companion Umar(RA) was known to be fierce with his sword, as well as the prophets uncle, Abbaas(RA) and not least Muawwiya(RA). I guess that the Arabs had developed their own form of sword fighting. Interesting question. Thank you for sharing your thoughts.