I've got a finite element problem involving paths around the interior of a torus. For this particular problem I think I could make things more computationally efficient if each cell in the mesh made a complete revolution of the torus. Here's a picture that might help illustrate:

http://upload.wikimedia.org/wikipedia/commons/5/54/Torus_cycles.png

The grey cells here make up a pretty typical mesh over the torus. I'd prefer to get away from that and move to a mesh where each cell is an interior neighborhood around some radius like the pink one. More general than the pink line would be interesting too... what about paths around the interior of the torus that are tilted relative to the axis, or oval or similar?

I'm not even sure what topic areas would discuss this type of problem. Are there any papers or textbooks out there that would help me out?