Without additional boundary conditions that constrain the wavefield at the boundaries of the computational domain, the wave equation does not obey a unique solution.
All boundary conditions are defined on so-called side sets of the mesh. A side set is just a way to flag edges (in 2D) or faces (in 3D) of a mesh and to give these a name. This is important, whenever different conditions are applied on different parts of the boundary of the domain.
The example mesh below has 4 side sets, each denoting one side of the mesh. The actual names are arbitrary and mesh dependent.
Common defaults for labelling the boundaries are
y1, and additionally
r0for the inner radius (if present),
r1for the outer radius,
In the following, denotes a side set where a certain boundary condition is imposed.
Without explicitly specifying boundary conditions, the spectral-element method will fall back to the natural boundary conditions.