checkpointing test with LA::distributed::Vector

[tjhei]

This adds a failing test for checkpointing using SolutionTransfer in parallel with LA::distributed::Vector. The problem is that we set values in

dealii/source/distributed/solution_transfer.cc

Lines 425 to 427 in dc06245

	cell->set_dof_values_by_interpolation(*it_input,
	*(*it_output),
	fe_index);

and then call compress(Insert):

dealii/source/distributed/solution_transfer.cc

Line 258 in dc06245

(*it)->compress(::dealii::VectorOperation::insert);

which is not supported using this vector type.

[tjhei]

@kronbichler here it is. Do you have a suggestion? I know that we set values more than once for a continuous FE, so using Add is not an option without keeping track of how many times we set the values.
Naive suggestion: allow compress(Insert) to work by ignoring NaN and fill all ghost values with NaN before setting values.

[kronbichler]

This reveals a more general problem that has bothered me for a long time. Depending on the VectorOperation passed to compress, we perform different actions in either our own vector or external classes. I like the suggestion of using NaN as some initial condition to the vector entries. This is a step we would need to do with the Vector type before we start the operation inserting the elements, mirroring the compress() call in the end. In other words, I think for a clean solution we would need to use Vector::set_neutral_element(vector_operation) before the loop over cells, and call compress(vector_operation) in the end with the same vector_operation. This is because also other VectorOperation choices, e.g. min or max, are actually not happy with our default value of operator=(0.), as setting all entries to 0 is only the neutral element for add. min would need std::numeric_limits<Number>::max() and max would need -std::numeric_limits<Number>::max() in order to make consistent arguments. What do think about this general solution? If we agree, we could work towards this goal in several steps, as the current PR is rather a symptom of a larger underlying problem.

[tjhei]

Yes, this is exactly what I was thinking about. It makes sense that we can generalize to min/Max, etc..
Is this too big of a change? I think this could be quite useful...

[bangerth]

Yes, I think too that that is the right direction to go!

[kronbichler]

OK, I'm glad we agree here. How should we proceed? I could work on this functionality for LA::d::Vector first on a separate branch, and then we try to use it here?

[tjhei]

I appreciate your help! If you want to help, maybe we start with the implementation of set_neutral_element(Insert) and then I can test it here.
Instead of introducing a new function, we could also reuse zero_out_ghost_values by adding the vectoroperation as an argument (with default Add). The name is okay in my opinion (it is the "zero" or neutral element for the operation).