Assigning material parameter to a group of elements without using geometric boundary

Hi Everyone, 

Does anyone know a way to group some elements (without using geometric boundary) and assign a parameter to it?

The goal is to just assign the parameter if the elements located inside a set of coordinates while keeping the uniformity and the quality of the mesh. 

Below is the illustrative example of it.

In my experience, adding a geometric boundary might reduce the quality of the mesh, especially near the sharp edges.

 Thanks everyone!