I use Microplanes, the medium one is great for Ginger or Garlic. These do not grate but have a shaving action, so you don't have to worry about the fibre issue. The Microplane was originally invented for woodwork! It looks like a grater but it has lots of tiny blades that have been etched out by a laser. They cost anything from ?19 - ?25, and you can get a version with multiple/exchangeable blades. Much better than your standard grater.
Happy (safe) cooking
CP