Unique FE evaluation on arbitrary points
David
I'm currently looking for a way to evaluate my global solution on an arbitrary cloud of points and stumbled across the (new) class `Utilities::MPI::RemotePointEvaluation<dim>`. In general, the class does exactly what I want with one particular exception; I want to evaluate each point out of the cloud only once in case of a distributed triangulation. If I understand it correctly this property is fulfilled in case the boolean function `is_map_unique()` returns true, but I don’t see any option to filter or tell the class that I actually want the map to be unique.
Assuming that the class cannot handle this case I tried to pre-filter the vertices by hand: For me, the most natural choice to fulfill the unique evaluation of the points is to assign them to a process, so that I only work on ‘locally owned vertices’. I compute a bounding box using the iterator filter `LocallyOwnedCell()`, filter the received cloud of points on the process and finally plug them into the `RemotePointEvaluation`. However, this does not work in case points of the cloud are located at the boundary of the bounding box, because they will technically be part of both bounding boxes of the involved processes. I would probably need to go a step further and implement a consensus algorithm in order to decide only for one specific process, which seems not trivial to me.
Before starting now to implement a more advanced solution I would like to ask if there is an obvious way I’m not aware of. Is it possible to enforce a unique evaluation using one of the ‘PointEvaluation’ classes or is it possible to let deal.II decide for an owner of an arbitrary vertex? I have also seen the function ‘find_active_cell_around_point()’ which might help, but it might end up in similar problem as well.
Thanks in advance
and best regards,
David
Peter Munch
Hi David,
> I want to evaluate each point out of the cloud only once in case of a distributed triangulation.
A quick (and dirty) solution would be to evaluate and perform the communication non-uniquely and pick out one of the received values at the end. See also VectorTools::evaluate_at_points() and the flag VectorTools::EvaluationFlags::insert: although intentionally not documented this function will take the first value of the process with the lowest rank.
> I would probably need to go a step further and implement a consensus algorithm in order to decide only for one specific process, which seems not trivial to me.
You are right. One would need an additional communication step
(with or without CA) to make the evaluation/communication more
efficient. I was thinking about introducing an additional flag to
the constructor of RemotePointEvaluation, but have not implemented
it yet, since in our use cases we either need the average values
(DG) or we set up the communication pattern in every time step due
to some very dynamic systems (multi phase flow).
Anyway, I am happy to discuss how to implement the needed
feature. The code that would need to be touched is:
https://github.com/dealii/dealii/blob/654b14481eeff7e744297025ea2078ab115611ac/source/grid/grid_tools.cc#L5905-L5909,
i.e., a consistent modification of send_components and
recv_components. I am happy to write a draft if you want.
Hope this helps,
Peter
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