Hello! In my inverse problem setup with deal.ii I set up an "observation" operator that acts on my solution vector to give the FE solution at a given set of grid points. I do this using FEFieldFunction for each point on this "observation" grid: all observation points are inside my domain of course, I identify the active cells that contain the points, and then for each point I evaluate the FE solution using FEFieldFunction::value.
Now that that is set up, I need the adjoint of this (linear?) operator. That is, beginning from the FE solution value at a point, I want to map to the space of my numerical solution (R^n_DOFS). As far as I can see in the deal.II API, FEFieldFunction does the following: 1. maps the active cell that contains the point to the unit cell 2. builds a 1-point custom quadrature rule for that point using the Quadrature<dim>::Quadrature(Point) constructor (weight of that point is = 1) 3. evaluates the FE solution at the point using the FEValues::value function and the quadrature. How would I go about building the transpose of this (implicit) point-solution evaluation operator? Say I have only one observation point. I can get the point where my quadrature is evaluated by calling FEFieldFunction::compute_point_locations(), right? How do I get the DoFs that are associated with the active cell that contains the point, and how exactly do they (the DoFs) come into play when the function gets evaluated? Does FEFieldFunction use DoFs for evaluation other than those associated with the active cell? many thanks! -- Mihai
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