I did try looking over what you had linked, but the material felt too complicated for me to comprehend. I’ve not heard of a restriction operator before, and the problem in the example was well beyond most problems I’ve seen before. So, I decided to set this material aside for future reference, and keep searching around.
Doing some further searching, I came across THIS PROBLEM. Now that I have seen how to cumulatively integrate an interpolated expression on a 1D mesh, I think that what I now need to do to accomplish the same thing for a 2D mesh is quite similar to what @Ramiro_Irastorza was trying to do when going from the parent mesh to a sub-mesh. For my specific problem, I wanted to, in an iterative procedure, do the following
- Find the solutions to a pair of problems on a parent mesh
- Use the solutions to obtain a new field
- Cumulatively integrate that field on the boundaries
- Let the results of those cumulative integrals be the boundary values to a new problem
I think what I need to do in order for 3 to work is take the expression interpolated onto the 2D space, and then interpolate that onto a 1D sub-space. Focusing just on the southern boundary of the square mesh, once the original function that was interpolated onto the full domain has been interpolated onto a subspace on the boundary, I think I should be able to do the same cumulative integration; that is what I will attempt to do from here. If you have any thoughts on my plan of action, or you think that this will not work, please feel free to share them with me!