I need a function to be defined as piecewise constant, and its support needs to be quite accurate for my computations.
As a simple example, consider as a domain the unit disk $\mathbb{D}$ and consider a ball $B_r$, then I would like to have something like $u = C_1$ on $B_r$ and $u = C_2$ on $\mathbb{D}\setminus B_r$.
I am aware that it is possible to refine mesh in Fenics, however this is NOT what I am looking for, since it would result in a very fine mesh at the inclusion (and I do not want it to slow down my computations).
In mshr, it is easy to define a hole in a domain, say
dom = Circle(Point(0,0),1)
ball = Circle(center,radius)
geometry = dom - ball
However I have not been able to force the mesh generation to use the boundary of the ball for
geometry = dom + ball
since the ball is already inside the domain. It seems like if you have:
dom = Circle(Point(0,0),1)
ball1 = Circle(center,radius-1e-2)
ball2 = Circle(center,radius+1e-2)
geometry = dom - ball2 + ball1
then you can get something close to what I seek, which is refined near the boundary of the ball inclusion. But somehow I need to repair the hole in the domain between ball1 and ball2, so is there some way to collapse vertices that are close to one another?
