Not adapter, but simply a different cable will do it! (or do you mean a simple connector adapter?, an active converter isn't needed!)
HDMI and DVI-D are very much the same, although they use different connectors. Only HDMI also supports sound, and DVI-D does not.
do make sure your monitor has DVI-D, not just DVI-A.
you might want to read http://elinux.org/RPi_config.txt.
in case you want the PI to force HDMI mode, if your monitor isn't recognized, also see the troubleshooting section in the wiki.