Support ufl.interpolate

[jorgensd]

Resolve #827

[michalhabera]

This looks very useful. Can you maybe provide a summary of how this is implemented and limitations in the overview, once ready?

[jorgensd]

This looks very useful. Can you maybe provide a summary of how this is implemented and limitations in the overview, once ready?

Of course. I’m not quite happy with the naming etc yet, so I’ll let it simmer for a few days.

I would also like to embed this with re-exposing cell and facet averages, which I started prior to this in: https://github.com/FEniCS/ffcx/tree/dokken/cell_avg_v2

Short story for now is:

1. we traverse the form for all interpolate operations.
2. For each interpolate, replace it with an overloaded ufl coefficient (proxycoefficient, should maybe be called intermediate coefficient?). This new coefficient stores a reference to should be interpolated into it.
3. Add an expression evaluating at interpolation points to the ufl objects from the analysis.
4. Standard dag traversal of new form.
5. We split now between coefficients from input form and those internal ones (they will be ordered at the end of reduced_coefficients due to their count being higher).
6. Generate expression evaluating at interpolation points
7. Within code generation extract standard coefficient data required by the new coefficients. Call expression tabulate.
8. if interpolation is not identity apply interpolation matrix multiplication, else copy into coefficient array used by the tabulator.
9. assemble tensor with coeffs and proxy coeffs.

[coveralls]

coverage: 85.226% (+0.6%) from 84.674% — dokken/proxy-coefficients into main