There are two or three things that should work:
 
Buy the clear plastic carpet runners at a hardware store, cut to fit, and
tape down.
 
A few places sell door-shaped mats (made out of the same stuff the mats
for under office chairs are made from).  I have a couple of those, but the
person I bought them from no longer supplies them.  If you can't find any
place that sells them, go to an office supply store, buy the mats for under
chairs and a good, sturdy matt knife and cut them to fit.
 
Another thing I've found works well is buying high quality plexiglas and
have it cut to the width of the door and have it over lap 6 to 8 inches on
both sides of the door.  I have this at one doorway where a mat won't fit,
and it is working very well!
 
Pat
[Posted in FML issue 3122]