All,
Currently our adjoints framework assembles the discrete adjoint
problem by transposing the matrix representing the discrete forward
problem. This is simple and works as long as we have (or only desire)
the discrete adjoint for an adjoint consistent formulation. Of course,
this might not be the case for all problems.
In particular, while computing boundary QoIs that are ill-posed due to
regularity issues, one might want to follow the approach described in
a paper by Giles, Larson et al. Here one imposes a Dirichlet bc for
the adjoint problem on the boundary in question, modifying the trial
space. This ensures that we are solving a well posed adjoint problem.
One way of extending the current framework to include such adjoint
formulations would be to have the user specify a side_qoi_constraint
along the lines of side_qoi_derivative and side_constraint. The user
would specify the stiffness matrix entries (penalty terms) for the
Dirichlet bc in side_qoi_residual and the corresponding residual term
in side_qoi_derivative. We can then include side_qoi_constraint in the
assembly before solving the adjoint.
Does this sound reasonable ? Of course any other ideas are welcome.
Thanks.
--
Vikram Garg
PhD Candidate
Institute for Computational and Engineering Sciences
The University of Texas at Austin
http://users.ices.utexas.edu/~vikram/
http://www.runforindia.org/runners/vikramg
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