Dear all, 

I want to differentiate my pde solution U with respect to some design 
variables E, that is, computing the Jacobian dU/dE. 
I already implemented the Jacobian analytically, however, I would like to 
double check it using AD. 

" (In theory an entire program could be made differentiable. This could be 
useful in, for example, the sensitivity analysis of solutions with respect 
to input parameters. However, to date this has not been tested.)"

I found this information in the AD module. 
Also the relevant tuturials -- step33, step 70, step 71 -- do not cover the 
topic sensitivity analysis, but only AD at cell- and quadrature point 
level. 

That said, is it possible (with reasonable efforts) to make the entire 
dealii program AD differentiable, or is it recommendable to use other open 
source tools for that purpose?
My biggest concern is the solution of the linear system because the solver 
classes require in most cases a Vector<double> and, consequently, the 
dependency u(E) can not be encoded.


Best
Simon

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