Hi, deal.ii developers and users

Recently, I get this question as been mentioned in subject.

I have a saddle point problem on hand. The system of vector-valued PDEs is 
non-linear. I implement the solver with Newton iteration without line 
search. And I also need to set up a specific initial configuration for 
iteration.  

Here comes the question, I don't have clear idea how to access and write 
down a specific value on the 0-th solution vector according to every Dof's 
geometric location on grid.  

Let's say we have a 3-components vector-valued unknown. Geometry domain is  
2 * 2 * 2 size cube.  I want to set Dofs, which are inside ball 
x^2+y^2+z^2=1,  to be  (1, 1, 1) at every vertex. While the rest of Dofs of 
the cube to be (1,0,0) at very vertex. 

I went through docs of DoFHandler,  DoFTools, ComponentMask and 
CellAccessor. Unfortunately, I only figured out that I can access certain 
DoFs in solution vector by loop over IndexSet, which is generated by 
DoFTools::extract_dofs(DofHandler., ComponentMask). I still no idea how to 
control the access through geometric information i.g., vertex's coordinates.

Is there any clue or idea how this could be done?

Best,
Timo

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