Applications of manifolds: mesh generation

Manifolds offer a generalisation to the modelling procedure, where the domain of an electromagnetic boundary value problem is a subset of a particular coordinate system. First of all, instead of identifying the points of the domain with coordinates, manifolds implement the principle that coordinates are not canonical. Second, in manifolds the coordinates are deliberately not bound by the distances between the points of the domain they represent. Finally, a manifold does not need to be coverable by a single coordinate system, but by several. These basic properties of manifolds make it possible to choose a coordinate system or systems that alleviate mesh generation problems caused by limited accuracy of floating point numbers. The authors propose three practical mesh generation-friendly problem representations.