Better ProcessedVariable

@TomTranter has pointed out several times that processed variables need a rethink and I agree. In particular we need to strike the balance between having to pass lots of inputs to ProcessedVariable and storing too much inside the variable object itself. However, we could switch to something better by doing e.g.

voltage = model.variables["Terminal voltage [V]"].process(solution)

where the mesh is stored in the variable and .process created a ProcessedVariable. Or something else? Like

processed_variables = model.process(["Terminal voltage [V]"], solution)

[tinosulzer]

Processed variable does 2 things:

1. Transform column vectors into n-dimensional arrays (up to 5 as you pointed out). Within the model everything is stored as a column vector (e.g. all the particle concentrations are stacked on top of each other), for speed, so it all has to be reshaped at the end in order to get the n-dimensional variables
2. Set up interpolation, which helps to abstract away having to worry about indices, which of the 5 dimensions corresponds to which, etc

Would the following be ok?

solution["Voltage"] # this is the ProcessedVariable class, with interpolation
solution["Voltage"].data # gives the n-dimensional matrix you want
solution.data # gives dictionary of n-dimensional arrays
solution.save(filename) # saves only the data arrays, to a dictionary

[tinosulzer]

Yes that sounds like the best way forward. We could also have the default being “don’t process any variables in solution” and then have a solution.update(variables) (or .process or .set) which processes any variables using the existing t and y. I think simulation is still useful and separate for everything leading up to obtaining the solution