Poisson Eqn in a concentric cube

[#DOMINIC DENVER JOHN CHANDAR#]

Hi,
 
     I would like to solve the Poisson equation (3D) in a concentric
type of cube as in the attached figure using PETSc. The solution domain
would be the shaded region only and it extends inside the cube. I would
like to have suggestions on ways to form and assemble the matrix
associated with the discretization. Also, is it a good practise to
discretize the entire domain and blank the grid points which are within
the cube not in the domain ?
 
Regards,
Dominic
 
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