Material Properties are assigned to 0

Dear Community,

In my thermal problem, I am assigning the material property to 0 at a certain section of my mesh in order to not have any influence of this section in my computation. My code and results everything is perfect thanks to freefem.

However, I have a more general question. As around 20% of my mesh has thermal property as 0, so it might give a highly sparse matrix. Other commercial codes generally crash doing such type of simulation, however, freefem is working perfectly. I wonder what is the justification behind this?

Thanks in advance;

It is hard to given a answer without the math. formulation.