Hello all,

I have a question concerning the use of deal.ii for the solution of a set of 
discrete KKT equations. I have derived the set of 3 discrete equations 
(primal/dual/optimality with discontinuous Galerkin) and I would like to 
implement and solve the whole system using some preconditioned linear solver 
(the all-at-once approach). My system looks as follows:

Au + B \lambda + C q = RHS1
Du + E \lambda + F q = RHS2
Hu + J \lambda + K q = RHS3

My vector of unknowns is [u \lambda q] (state, dual, and controls). My guess is 
I should make use of the vector-valued approach, but I can't quite figure out 
where to start from since in the tutorials we start from a strong-form system 
and then reduce it to a single equation in weak form; whereas, in my case, I 
have 3 equations that have already been discretized (and starting from the 
continuous weak/strong form is not an option). How can I go about making this 
work?

Another way to go about this I guess would be to assemble each sparse 
sub-matrix 
A,B,...K and the 3 RHS terms, and then put them in a larger block matrix... is 
that possible with deal.ii? Would it be simpler than the vector valued approach?

Thanks a lot for your guidance! your help is very much appreciated :)

Best, 
  -- Mihai

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