Hello Wofgang, just to clear things up in my mind: the way to go from the KKT system (eqns 2.8-2.10 in your paper) for the cost function J to a single discrete bilinear form (for implementation) is to re-cast the original system into one that looks like equation (4.1) and then apply Gauss-Newton to this formulation (eqn 5.1-5.2)?
I am going for "discretize-then-optimize" so my KKT system is already in discrete form (DG) to begin with. thank you, -- Mihai ________________________________ Von: Wolfgang Bangerth <[email protected]> An: [email protected] CC: mihai alexe <[email protected]> Gesendet: Samstag, den 8. Januar 2011, 17:41:48 Uhr Betreff: Re: [deal.II] solve optimality system with DG & deal.ii > 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? In order to build the system of equations you need to cast this in a single bilinear form. To see how to do this, you may want to take a look at my paper in SISC, see number 23 here: https://www.math.tamu.edu/~bangerth/publications.html#x-reviewed The paper also has a discussion on how to solve the linear problems. On the other hand, if your system is small enough, you could also use SparseDirectUMFPACK to solve it. Best W. ------------------------------------------------------------------------- Wolfgang Bangerth email: [email protected] www: http://www.math.tamu.edu/~bangerth/
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