Hi again, in regard to the previous message - I found out I have to make my problem a bit more complicated, and now the KKT system yields a nonlinear discrete problem. Instead of the formulation below, I now have something like
F (u, \lambda, q) = [RHS1; RHS2; RHS3]^T Should I go for the vector valued approach when coding up the function F? I then want to implement Newton's method with either finite differences, or (preferably) automatic differentiation derivatives (thinking to follow the tutorial and use Sacado). Again, my system has 3 discrete equations; how could I cast this in the vector-valued framework given in the tutorial? again, thank you. -- Mihai ________________________________ Von: mihai alexe <[email protected]> An: deal.ii <[email protected]> CC: mihai alexe <[email protected]> Gesendet: Freitag, den 7. Januar 2011, 15:12:16 Uhr Betreff: solve optimality system with DG & deal.ii 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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