Caching of Ad evalutaions

[keileg]

This issue is a coordinating issue for improvements of the planned AdParser class to be implemented in #1181 and is downstream from that issue. Right now, this is just a bank of ideas.

Caching and recomputations

Part of the motivation for introducing the AdParser is to be able to cache evaluations of Ad operator trees, or subtrees. A key step will be to identify which subtrees can be regarded as static between non-linear iterations, time steps etc.; for clarity the decision on how and whether to do caching for specific terms is a different matter. Some rules of thumb will clearly apply:

1. Variables change between non-linear iterations (with a possible exception if we implement splitting schemes on the non-linear level, but that would require the introduction of a notion of active/passive variables or similar).
2. Discretizations change if the term is non-linear. The model will know about this.
3. Time-dependent dense arrays can change between time steps, but not inside the non-linear solver.
4. Grid-related quantities change if the grid changes, e.g. for AMR, fracture propagation, or large deformation. The user setting up the model should know about this.

A pragmatic approach to detecting changed and unaltered Ad operator trees could be to define a tagging system (an Enum?) which describes the above classification scheme, or similar, and assign tags to individual operators.

TBC.