Hello,
The original work dates back to 1997 and was done by Reinhardt Hinkelmann as a PhD thesis, it is reference [101] in my book.
The Lagrangian part was done later, firstly by Jacek Jankowski at BAW in Germany, and completed till about 2012 at EDF lab LNHE in France, but this was never published. As a matter of fact, there is no theoretical issue, it is "just" computer engineering. In the Lagrangian part (computing pathlines) we now ensure that there is not even a digit of difference between sequential and parallel runs. There is now a PhD on the way that aims at the same result for all parts of the code.
With best regards,
Jean-Michel Hervouet
With best regards,
Jean-Michel Hervouet