residual calculation needs to be done when boundary degrees of freedom have not been removed (since their removal takes place in the Mult step in order to introduce the proper restoring force). Whereas jacobian calculation needs to always work from the boundary aware operators (these are sparse matrices)
The other thing to note here is that this seems contrary to a matrix free design. While true it is common practive to assemble linear terms since they are cheap. We still never assemble the non linear matrix form.
In order to maintain memory efficienty I have implimented a matrix free SchurComplement operator as well as an operator which uses a few iterations of GMRES to approxinate the inverse of any general operator.
the preconditioner must be built once before the solver begins to iterater, by putting the logic for this in a dedicated method it becomes cleaner to call
working on a "smart" schur compliment preconditioner for the block form of the lane emden equation. Currently this is stub and should not be considered usable
essential dofs can be applied to both theta and phi (grad theta) if we move to a block form. I have done this derivation and made that change so that we can properly apply the central boundary condition to the slope
